Description

8.321 is the first semester of a two-semester subject on quantum theory, stressing principles. Topics covered include: Hilbert spaces, observables, uncertainty relations, eigenvalue problems and methods for solution thereof, time-evolution in the Schrodinger, Heisenberg, and interaction pictures, connections between classical and quantum mechanics, path integrals, quantum mechanics in EM fields, angular momentum, time-independent perturbation theory, density operators, and quantum measurement. 8.321 is the first semester of a two-semester subject on quantum theory, stressing principles. Topics covered include: Hilbert spaces, observables, uncertainty relations, eigenvalue problems and methods for solution thereof, time-evolution in the Schrodinger, Heisenberg, and interaction pictures, connections between classical and quantum mechanics, path integrals, quantum mechanics in EM fields, angular momentum, time-independent perturbation theory, density operators, and quantum measurement.

Subjects

eigenstates | eigenstates | uncertainty relation | uncertainty relation | observables | observables | eigenvalues | eigenvalues | probabilities of the results of measurement | probabilities of the results of measurement | transformation theory | transformation theory | equations of motion | equations of motion | constants of motion | constants of motion | Symmetry in quantum mechanics | Symmetry in quantum mechanics | representations of symmetry groups | representations of symmetry groups | Variational and perturbation approximations | Variational and perturbation approximations | Systems of identical particles and applications | Systems of identical particles and applications | Time-dependent perturbation theory | Time-dependent perturbation theory | Scattering theory: phase shifts | Scattering theory: phase shifts | Born approximation | Born approximation | The quantum theory of radiation | The quantum theory of radiation | Second quantization and many-body theory | Second quantization and many-body theory | Relativistic quantum mechanics of one electron | Relativistic quantum mechanics of one electron | probability | probability | measurement | measurement | motion equations | motion equations | motion constants | motion constants | symmetry groups | symmetry groups | quantum mechanics | quantum mechanics | variational approximations | variational approximations | perturbation approximations | perturbation approximations | identical particles | identical particles | time-dependent perturbation theory | time-dependent perturbation theory | scattering theory | scattering theory | phase shifts | phase shifts | quantum theory of radiation | quantum theory of radiation | second quantization | second quantization | many-body theory | many-body theory | relativistic quantum mechanics | relativistic quantum mechanics | one electron | one electron | Hilbert spaces | Hilbert spaces | time evolution | time evolution | Schrodinger picture | Schrodinger picture | Heisenberg picture | Heisenberg picture | interaction picture | interaction picture | classical mechanics | classical mechanics | path integrals | path integrals | EM fields | EM fields | electromagnetic fields | electromagnetic fields | angular momentum | angular momentum | density operators | density operators | quantum measurement | quantum measurement | quantum statistics | quantum statistics | quantum dynamics | quantum dynamics

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8.322 is the second semester of a two-semester subject on quantum theory, stressing principles. Topics covered include: time-dependent perturbation theory and applications to radiation, quantization of EM radiation field, adiabatic theorem and Berry's phase, symmetries in QM, many-particle systems, scattering theory, relativistic quantum mechanics, and Dirac equation. 8.322 is the second semester of a two-semester subject on quantum theory, stressing principles. Topics covered include: time-dependent perturbation theory and applications to radiation, quantization of EM radiation field, adiabatic theorem and Berry's phase, symmetries in QM, many-particle systems, scattering theory, relativistic quantum mechanics, and Dirac equation.

Subjects

uncertainty relation | uncertainty relation | observables | observables | eigenstates | eigenstates | eigenvalues | eigenvalues | probabilities of the results of measurement | probabilities of the results of measurement | transformation theory | transformation theory | equations of motion | equations of motion | constants of motion | constants of motion | Symmetry in quantum mechanics | Symmetry in quantum mechanics | representations of symmetry groups | representations of symmetry groups | Variational and perturbation approximations | Variational and perturbation approximations | Systems of identical particles and applications | Systems of identical particles and applications | Time-dependent perturbation theory | Time-dependent perturbation theory | Scattering theory: phase shifts | Scattering theory: phase shifts | Born approximation | Born approximation | The quantum theory of radiation | The quantum theory of radiation | Second quantization and many-body theory | Second quantization and many-body theory | Relativistic quantum mechanics of one electron | Relativistic quantum mechanics of one electron | probability | probability | measurement | measurement | motion equations | motion equations | motion constants | motion constants | symmetry groups | symmetry groups | quantum mechanics | quantum mechanics | variational approximations | variational approximations | perturbation approximations | perturbation approximations | identical particles | identical particles | time-dependent perturbation theory | time-dependent perturbation theory | scattering theory | scattering theory | phase shifts | phase shifts | quantum theory of radiation | quantum theory of radiation | second quantization | second quantization | many-body theory | many-body theory | relativistic quantum mechanics | relativistic quantum mechanics | one electron | one electron | quantization | quantization | EM radiation field | EM radiation field | electromagnetic radiation field | electromagnetic radiation field | adiabatic theorem | adiabatic theorem | Berry?s phase | Berry?s phase | many-particle systems | many-particle systems | Dirac equation | Dirac equation | Hilbert spaces | Hilbert spaces | time evolution | time evolution | Schrodinger picture | Schrodinger picture | Heisenberg picture | Heisenberg picture | interaction picture | interaction picture | classical mechanics | classical mechanics | path integrals | path integrals | EM fields | EM fields | electromagnetic fields | electromagnetic fields | angular momentum | angular momentum | density operators | density operators | quantum measurement | quantum measurement | quantum statistics | quantum statistics | quantum dynamics | quantum dynamics

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Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see http://ocw.mit.edu/terms/index.htm

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This class covers topics in time-dependent quantum mechanics, molecular spectroscopy, and relaxation, with an emphasis on descriptions applicable to condensed phase problems and a statistical description of ensembles. This class covers topics in time-dependent quantum mechanics, molecular spectroscopy, and relaxation, with an emphasis on descriptions applicable to condensed phase problems and a statistical description of ensembles.

Subjects

introductory quantum mechanics | introductory quantum mechanics | time-dependent quantum mechanics | time-dependent quantum mechanics | spectroscopy | spectroscopy | perturbation theory | perturbation theory | two-level systems | two-level systems | light-matter interactions | light-matter interactions | correlation functions | correlation functions | linear response theory | linear response theory | nonlinear spectroscopy | nonlinear spectroscopy

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5.74 explores time-dependent quantum mechanics and spectroscopy. Topics covered include: perturbation theory, two-level systems, light-matter interactions, relaxation in quantum systems, correlation functions and linear response theory, and nonlinear spectroscopy. The instructor would like to acknowledge Anne Hudson for assisting in preparation of the 5.74 notes. 5.74 explores time-dependent quantum mechanics and spectroscopy. Topics covered include: perturbation theory, two-level systems, light-matter interactions, relaxation in quantum systems, correlation functions and linear response theory, and nonlinear spectroscopy. The instructor would like to acknowledge Anne Hudson for assisting in preparation of the 5.74 notes.

Subjects

introductory quantum mechanics | introductory quantum mechanics | time-dependent quantum mechanics | time-dependent quantum mechanics | spectroscopy | spectroscopy | perturbation theory | perturbation theory | two-level systems | two-level systems | light-matter interactions | light-matter interactions | correlation functions | correlation functions | linear response theory | linear response theory | nonlinear spectroscopy | nonlinear spectroscopy

License

Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see http://ocw.mit.edu/terms/index.htm

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This course covers topics in time-dependent quantum mechanics, spectroscopy, and relaxation, with an emphasis on descriptions applicable to condensed phase problems and a statistical description of ensembles. This course covers topics in time-dependent quantum mechanics, spectroscopy, and relaxation, with an emphasis on descriptions applicable to condensed phase problems and a statistical description of ensembles.

Subjects

introductory quantum mechanics | introductory quantum mechanics | time-dependent quantum mechanics | time-dependent quantum mechanics | spectroscopy | spectroscopy | perturbation theory | perturbation theory | two-level systems | two-level systems | light-matter interactions | light-matter interactions | correlation functions | correlation functions | linear response theory | linear response theory | nonlinear spectroscopy | nonlinear spectroscopy

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This course covers time-dependent quantum mechanics and spectroscopy. Topics include perturbation theory, two-level systems, light-matter interactions, relaxation in quantum systems, correlation functions and linear response theory, and nonlinear spectroscopy. This course covers time-dependent quantum mechanics and spectroscopy. Topics include perturbation theory, two-level systems, light-matter interactions, relaxation in quantum systems, correlation functions and linear response theory, and nonlinear spectroscopy.

Subjects

introductory quantum mechanics | introductory quantum mechanics | time-dependent quantum mechanics | time-dependent quantum mechanics | spectroscopy | spectroscopy | perturbation theory | perturbation theory | two-level systems | two-level systems | light-matter interactions | light-matter interactions | correlation functions | correlation functions | linear response theory | linear response theory | nonlinear spectroscopy | nonlinear spectroscopy

License

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The theoretical frameworks of Hartree-Fock theory and density functional theory are presented in this course as approximate methods to solve the many-electron problem. A variety of ways to incorporate electron correlation are discussed. The application of these techniques to calculate the reactivity and spectroscopic properties of chemical systems, in addition to the thermodynamics and kinetics of chemical processes, is emphasized. This course also focuses on cutting edge methods to sample complex hypersurfaces, for reactions in liquids, catalysts and biological systems. The theoretical frameworks of Hartree-Fock theory and density functional theory are presented in this course as approximate methods to solve the many-electron problem. A variety of ways to incorporate electron correlation are discussed. The application of these techniques to calculate the reactivity and spectroscopic properties of chemical systems, in addition to the thermodynamics and kinetics of chemical processes, is emphasized. This course also focuses on cutting edge methods to sample complex hypersurfaces, for reactions in liquids, catalysts and biological systems.

Subjects

quantum mechanics | quantum mechanics | computational quantum mechanics | computational quantum mechanics | molecular systems | molecular systems | extended systems | extended systems | Hartree-Fock theory | Hartree-Fock theory | density functional theory | density functional theory | DFT | DFT | many-electron problem | many-electron problem | electron correlation | electron correlation | chemical systems | chemical systems | reactivity | reactivity | spectroscopic properties | spectroscopic properties | thermodynamics | thermodynamics | kinetics | kinetics | chemical processes | chemical processes | complex hypersurfaces | complex hypersurfaces | CPMD | CPMD | Car-Parrinello Molecular Dynamics | Car-Parrinello Molecular Dynamics | 10.675 | 10.675 | 5.675 | 5.675

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8.321 is the first semester of a two-semester subject on quantum theory, stressing principles. Topics covered include: Hilbert spaces, observables, uncertainty relations, eigenvalue problems and methods for solution thereof, time-evolution in the Schrodinger, Heisenberg, and interaction pictures, connections between classical and quantum mechanics, path integrals, quantum mechanics in EM fields, angular momentum, time-independent perturbation theory, density operators, and quantum measurement.

Subjects

eigenstates | uncertainty relation | observables | eigenvalues | probabilities of the results of measurement | transformation theory | equations of motion | constants of motion | Symmetry in quantum mechanics | representations of symmetry groups | Variational and perturbation approximations | Systems of identical particles and applications | Time-dependent perturbation theory | Scattering theory: phase shifts | Born approximation | The quantum theory of radiation | Second quantization and many-body theory | Relativistic quantum mechanics of one electron | probability | measurement | motion equations | motion constants | symmetry groups | quantum mechanics | variational approximations | perturbation approximations | identical particles | time-dependent perturbation theory | scattering theory | phase shifts | quantum theory of radiation | second quantization | many-body theory | relativistic quantum mechanics | one electron | Hilbert spaces | time evolution | Schrodinger picture | Heisenberg picture | interaction picture | classical mechanics | path integrals | EM fields | electromagnetic fields | angular momentum | density operators | quantum measurement | quantum statistics | quantum dynamics

License

Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see https://ocw.mit.edu/terms/index.htm

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8.322 is the second semester of a two-semester subject on quantum theory, stressing principles. Topics covered include: time-dependent perturbation theory and applications to radiation, quantization of EM radiation field, adiabatic theorem and Berry's phase, symmetries in QM, many-particle systems, scattering theory, relativistic quantum mechanics, and Dirac equation.

Subjects

uncertainty relation | observables | eigenstates | eigenvalues | probabilities of the results of measurement | transformation theory | equations of motion | constants of motion | Symmetry in quantum mechanics | representations of symmetry groups | Variational and perturbation approximations | Systems of identical particles and applications | Time-dependent perturbation theory | Scattering theory: phase shifts | Born approximation | The quantum theory of radiation | Second quantization and many-body theory | Relativistic quantum mechanics of one electron | probability | measurement | motion equations | motion constants | symmetry groups | quantum mechanics | variational approximations | perturbation approximations | identical particles | time-dependent perturbation theory | scattering theory | phase shifts | quantum theory of radiation | second quantization | many-body theory | relativistic quantum mechanics | one electron | quantization | EM radiation field | electromagnetic radiation field | adiabatic theorem | Berry?s phase | many-particle systems | Dirac equation | Hilbert spaces | time evolution | Schrodinger picture | Heisenberg picture | interaction picture | classical mechanics | path integrals | EM fields | electromagnetic fields | angular momentum | density operators | quantum measurement | quantum statistics | quantum dynamics

License

Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see https://ocw.mit.edu/terms/index.htm

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8.321 is the first semester of a two-semester subject on quantum theory, stressing principles. Topics covered include: Hilbert spaces, observables, uncertainty relations, eigenvalue problems and methods for solution thereof, time-evolution in the Schrodinger, Heisenberg, and interaction pictures, connections between classical and quantum mechanics, path integrals, quantum mechanics in EM fields, angular momentum, time-independent perturbation theory, density operators, and quantum measurement.

Subjects

eigenstates | uncertainty relation | observables | eigenvalues | probabilities of the results of measurement | transformation theory | equations of motion | constants of motion | Symmetry in quantum mechanics | representations of symmetry groups | Variational and perturbation approximations | Systems of identical particles and applications | Time-dependent perturbation theory | Scattering theory: phase shifts | Born approximation | The quantum theory of radiation | Second quantization and many-body theory | Relativistic quantum mechanics of one electron | probability | measurement | motion equations | motion constants | symmetry groups | quantum mechanics | variational approximations | perturbation approximations | identical particles | time-dependent perturbation theory | scattering theory | phase shifts | quantum theory of radiation | second quantization | many-body theory | relativistic quantum mechanics | one electron | Hilbert spaces | time evolution | Schrodinger picture | Heisenberg picture | interaction picture | classical mechanics | path integrals | EM fields | electromagnetic fields | angular momentum | density operators | quantum measurement | quantum statistics | quantum dynamics

License

Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see https://ocw.mit.edu/terms/index.htm

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8.322 is the second semester of a two-semester subject on quantum theory, stressing principles. Topics covered include: time-dependent perturbation theory and applications to radiation, quantization of EM radiation field, adiabatic theorem and Berry's phase, symmetries in QM, many-particle systems, scattering theory, relativistic quantum mechanics, and Dirac equation.

Subjects

uncertainty relation | observables | eigenstates | eigenvalues | probabilities of the results of measurement | transformation theory | equations of motion | constants of motion | Symmetry in quantum mechanics | representations of symmetry groups | Variational and perturbation approximations | Systems of identical particles and applications | Time-dependent perturbation theory | Scattering theory: phase shifts | Born approximation | The quantum theory of radiation | Second quantization and many-body theory | Relativistic quantum mechanics of one electron | probability | measurement | motion equations | motion constants | symmetry groups | quantum mechanics | variational approximations | perturbation approximations | identical particles | time-dependent perturbation theory | scattering theory | phase shifts | quantum theory of radiation | second quantization | many-body theory | relativistic quantum mechanics | one electron | quantization | EM radiation field | electromagnetic radiation field | adiabatic theorem | Berry?s phase | many-particle systems | Dirac equation | Hilbert spaces | time evolution | Schrodinger picture | Heisenberg picture | interaction picture | classical mechanics | path integrals | EM fields | electromagnetic fields | angular momentum | density operators | quantum measurement | quantum statistics | quantum dynamics

License

Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see https://ocw.mit.edu/terms/index.htm

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This class explores the changing roles of physics and physicists during the 20th century. Topics range from relativity theory and quantum mechanics to high-energy physics and cosmology. The course also examines the development of modern physics within shifting institutional, cultural, and political contexts, such as physics in Imperial Britain, Nazi Germany, U.S. efforts during World War II, and physicists' roles during the Cold War. This class explores the changing roles of physics and physicists during the 20th century. Topics range from relativity theory and quantum mechanics to high-energy physics and cosmology. The course also examines the development of modern physics within shifting institutional, cultural, and political contexts, such as physics in Imperial Britain, Nazi Germany, U.S. efforts during World War II, and physicists' roles during the Cold War.

Subjects

relativity theory | relativity theory | quantum mechanics | quantum mechanics | solid-state physics | solid-state physics | elementary particles | elementary particles | quarks | quarks | cosmology | cosmology | nuclear weapons | nuclear weapons | Maxwell | Maxwell | Mach | Mach | Poincar? | Poincar? | Bohr | Bohr | Heisenberg | Heisenberg | Schr?dinger | Schr?dinger | McCarthyism | McCarthyism | Einstein | Einstein | Planck | Planck | Feynman | Feynman | scientific frontiers | scientific frontiers

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This course presents the concepts and techniques for solving partial differential equations (pde), with emphasis on nonlinear pde. This course presents the concepts and techniques for solving partial differential equations (pde), with emphasis on nonlinear pde.

Subjects

partial differential equations (pde) | partial differential equations (pde) | nonlinear pde | nonlinear pde | Diffusion | Diffusion | dispersion | dispersion | Initial and boundary value problems | Initial and boundary value problems | Characteristics and shocks | Characteristics and shocks | Separation of variables | Separation of variables | transform methods | transform methods | Green's functions | Green's functions | Asymptotics | Asymptotics | geometrical theory | geometrical theory | Dimensional analysis | Dimensional analysis | self-similarity | self-similarity | traveling waves | traveling waves | Singular perturbation and boundary layers | Singular perturbation and boundary layers | Solitons | Solitons | Variational methods | Variational methods | Free-boundary problems | Free-boundary problems | fluid dynamics | fluid dynamics | electrical engineering | electrical engineering | mechanical engineering | mechanical engineering | materials science | materials science | quantum mechanics | quantum mechanics

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This course is offered to graduate students and covers topics in five major areas of quantum optical communication: quantum optics, single-mode and two-mode quantum systems, multi-mode quantum systems, nonlinear optics, and quantum systems theory. Specific topics include the following.  Quantum optics: Dirac notation quantum mechanics; harmonic oscillator quantization; number states, coherent states, and squeezed states; radiation field quantization and quantum field propagation; P-representation and classical fields.  Linear loss and linear amplification: commutator preservation and the Uncertainty Principle; beam splitters; phase-insensitive and phase-sensitive amplifiers. Quantum photodetection: direct detection, heterodyne detection, and homodyne detection.&a This course is offered to graduate students and covers topics in five major areas of quantum optical communication: quantum optics, single-mode and two-mode quantum systems, multi-mode quantum systems, nonlinear optics, and quantum systems theory. Specific topics include the following.  Quantum optics: Dirac notation quantum mechanics; harmonic oscillator quantization; number states, coherent states, and squeezed states; radiation field quantization and quantum field propagation; P-representation and classical fields.  Linear loss and linear amplification: commutator preservation and the Uncertainty Principle; beam splitters; phase-insensitive and phase-sensitive amplifiers. Quantum photodetection: direct detection, heterodyne detection, and homodyne detection.&a

Subjects

Quantum optics: Dirac notation quantum mechanics | Quantum optics: Dirac notation quantum mechanics | harmonic oscillator quantization | harmonic oscillator quantization | number states | coherent states | and squeezed states | number states | coherent states | and squeezed states | radiation field quantization and quantum field propagation | radiation field quantization and quantum field propagation | P-representation and classical fields | P-representation and classical fields | Linear loss and linear amplification: commutator preservation and the Uncertainty Principle | Linear loss and linear amplification: commutator preservation and the Uncertainty Principle | beam splitters | beam splitters | phase-insensitive and phase-sensitive amplifiers | phase-insensitive and phase-sensitive amplifiers | Quantum photodetection: direct detection | heterodyne detection | and homodyne detection | Quantum photodetection: direct detection | heterodyne detection | and homodyne detection | Second-order nonlinear optics: phasematched interactions | Second-order nonlinear optics: phasematched interactions | optical parametric amplifiers | optical parametric amplifiers | generation of squeezed states | photon-twin beams | non-classical fourth-order interference | and polarization entanglement | generation of squeezed states | photon-twin beams | non-classical fourth-order interference | and polarization entanglement | Quantum systems theory: optimum binary detection | Quantum systems theory: optimum binary detection | quantum precision measurements | quantum precision measurements | quantum cryptography | quantum cryptography | quantum teleportation | quantum teleportation

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Junior Lab consists of two undergraduate courses in experimental physics. The courses are offered by the MIT Physics Department, and are usually taken by Juniors (hence the name). Officially, the courses are called Experimental Physics I and II and are numbered 8.13 for the first half, given in the fall semester, and 8.14 for the second half, given in the spring.The purposes of Junior Lab are to give students hands-on experience with some of the experimental basis of modern physics and, in the process, to deepen their understanding of the relations between experiment and theory, mostly in atomic and nuclear physics. Each term, students choose 5 different experiments from a list of 21 total labs. Junior Lab consists of two undergraduate courses in experimental physics. The courses are offered by the MIT Physics Department, and are usually taken by Juniors (hence the name). Officially, the courses are called Experimental Physics I and II and are numbered 8.13 for the first half, given in the fall semester, and 8.14 for the second half, given in the spring.The purposes of Junior Lab are to give students hands-on experience with some of the experimental basis of modern physics and, in the process, to deepen their understanding of the relations between experiment and theory, mostly in atomic and nuclear physics. Each term, students choose 5 different experiments from a list of 21 total labs.

Subjects

Junior Lab | Junior Lab | experimental | experimental | atomic | atomic | nuclear | nuclear | physics | physics | optics | optics | photoelectric effect | photoelectric effect | poisson | poisson | statistics | statistics | electromagnetic pulse | electromagnetic pulse | compton scattering | compton scattering | Franck-Hertz experiment | Franck-Hertz experiment | relativistic dynamics | relativistic dynamics | nuclear magnetic resonance | nuclear magnetic resonance | spin echoes | spin echoes | cosmic-ray muons | cosmic-ray muons | Rutherford Scattering | Rutherford Scattering | emission spectra | emission spectra | neutron physics | neutron physics | Johnson noise | Johnson noise | shot noise | shot noise | quantum mechanics | quantum mechanics | alpha decay | alpha decay | radio astrophysics | radio astrophysics | Zeeman effect | Zeeman effect | rubidium | rubidium | M?ssbauer | M?ssbauer | spectroscopy | spectroscopy | X-Ray physics | X-Ray physics | superconductivity | superconductivity | Doppler-free | Doppler-free | laser | laser

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This course presents an introduction to quantum mechanics. It begins with an examination of the historical development of quantum theory, properties of particles and waves, wave mechanics and applications to simple systems -- the particle in a box, the harmonic oscillator, the rigid rotor and the hydrogen atom. The lectures continue with a discussion of atomic structure and the Periodic Table. The final lectures cover applications to chemical bonding including valence bond and molecular orbital theory, molecular structure, spectroscopy.AcknowledgementsThe material for 5.61 has evolved over a period of many years, and, accordingly, several faculty members have contributed to the development of the course contents. The original version of the lecture notes that are available on OCW was prepa This course presents an introduction to quantum mechanics. It begins with an examination of the historical development of quantum theory, properties of particles and waves, wave mechanics and applications to simple systems -- the particle in a box, the harmonic oscillator, the rigid rotor and the hydrogen atom. The lectures continue with a discussion of atomic structure and the Periodic Table. The final lectures cover applications to chemical bonding including valence bond and molecular orbital theory, molecular structure, spectroscopy.AcknowledgementsThe material for 5.61 has evolved over a period of many years, and, accordingly, several faculty members have contributed to the development of the course contents. The original version of the lecture notes that are available on OCW was prepa

Subjects

physical chemistry | physical chemistry | quantum mechanics | quantum mechanics | quantum chemistry | quantum chemistry | particles and waves; wave mechanics | particles and waves; wave mechanics | atomic structure | atomic structure | valence orbital | valence orbital | molecular orbital theory | molecular orbital theory | molecular structure | molecular structure | photochemistry | photochemistry | particles and waves | wave mechanics | particles and waves | wave mechanics

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This course introduces string theory to undergraduate and is based upon Prof. Zwiebach's textbook entitled A First Course in String Theory. Since string theory is quantum mechanics of a relativistic string, the foundations of the subject can be explained to students exposed to both special relativity and basic quantum mechanics. This course develops the aspects of string theory and makes it accessible to students familiar with basic electromagnetism and statistical mechanics.Technical RequirementsSoftware to view the .tex files on this course site can be accessed via the Comprehensive TeX Archive Network (CTAN) and the TeX Users Group Web site. Postscript viewer software, such as Ghostscript/Ghostview, can be used to view the .ps files found on this course site. This course introduces string theory to undergraduate and is based upon Prof. Zwiebach's textbook entitled A First Course in String Theory. Since string theory is quantum mechanics of a relativistic string, the foundations of the subject can be explained to students exposed to both special relativity and basic quantum mechanics. This course develops the aspects of string theory and makes it accessible to students familiar with basic electromagnetism and statistical mechanics.Technical RequirementsSoftware to view the .tex files on this course site can be accessed via the Comprehensive TeX Archive Network (CTAN) and the TeX Users Group Web site. Postscript viewer software, such as Ghostscript/Ghostview, can be used to view the .ps files found on this course site.

Subjects

string theory | string theory | quantum mechanics | quantum mechanics | relativistic string | relativistic string | special relativity | special relativity | electromagnetism | electromagnetism | statistical mechanics | statistical mechanics | D-branes | D-branes | string thermodynamics | string thermodynamics | Light-cone | Light-cone | Tachyons | Tachyons | Kalb-Ramond fields | Kalb-Ramond fields | Lorentz invariance | Lorentz invariance | Born-Infeld electrodynamics | Born-Infeld electrodynamics | Hagedorn temperature | Hagedorn temperature | Riemann surfaces | Riemann surfaces | fermionic string theories | fermionic string theories

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This course is a required sophomore subject in the Department of Materials Science and Engineering, designed to be taken in conjunction with the core lecture subject 3.012 Fundamentals of Materials Science and Engineering. The laboratory subject combines experiments illustrating the principles of quantum mechanics, thermodynamics and structure with intensive oral and written technical communication practice. Specific topics include: experimental exploration of the connections between energetics, bonding and structure of materials, and application of these principles in instruments for materials characterization; demonstration of the wave-like nature of electrons; hands-on experience with techniques to quantify energy (DSC), bonding (XPS, AES, FTIR, UV/Vis and force spectroscopy), and degre This course is a required sophomore subject in the Department of Materials Science and Engineering, designed to be taken in conjunction with the core lecture subject 3.012 Fundamentals of Materials Science and Engineering. The laboratory subject combines experiments illustrating the principles of quantum mechanics, thermodynamics and structure with intensive oral and written technical communication practice. Specific topics include: experimental exploration of the connections between energetics, bonding and structure of materials, and application of these principles in instruments for materials characterization; demonstration of the wave-like nature of electrons; hands-on experience with techniques to quantify energy (DSC), bonding (XPS, AES, FTIR, UV/Vis and force spectroscopy), and degre

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electron | electron | electronic properties | electronic properties | magnetism | magnetism | magentic properties | magentic properties | structure | structure | crystal | crystal | lattice | lattice | energy | energy | thermodynamics | thermodynamics | differential scanning calorimetry (DSC) | differential scanning calorimetry (DSC) | x-ray diffraction (XRD) | x-ray diffraction (XRD) | scanning probe microscopy (AFM | scanning probe microscopy (AFM | STM) | STM) | scanning electron microscopy (SEM) | scanning electron microscopy (SEM) | UV/Vis | UV/Vis | Raman spectroscopy | Raman spectroscopy | FTIR spectroscopy | FTIR spectroscopy | x-ray photoelectron spectroscopy (XPS) | x-ray photoelectron spectroscopy (XPS) | vibrating sample magnetometry (VSM) | vibrating sample magnetometry (VSM) | dynamic light scattering (DLS) | dynamic light scattering (DLS) | phonon | phonon | quantum | quantum | quantum mechanics | quantum mechanics | radiation | radiation | battery | battery | fuel cell | fuel cell | ferromagnetism | ferromagnetism | ferromagnetic | ferromagnetic | polymer | polymer | glass | glass | corrosion | corrosion

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6.728 covers concepts in elementary quantum mechanics and statistical physics. The course introduces applied quantum physics and  emphasizes an experimental basis for quantum mechanics. Concepts covered include: Schrodinger's equation applied to the free particle, tunneling, the harmonic oscillator, and hydrogen atom, variational methods, Fermi-Dirac, Bose-Einstein, and Boltzmann distribution functions, and simple models for metals, semiconductors, and devices such as electron microscopes, scanning tunneling microscope, thermonic emitters, atomic force microscope, and others. 6.728 covers concepts in elementary quantum mechanics and statistical physics. The course introduces applied quantum physics and  emphasizes an experimental basis for quantum mechanics. Concepts covered include: Schrodinger's equation applied to the free particle, tunneling, the harmonic oscillator, and hydrogen atom, variational methods, Fermi-Dirac, Bose-Einstein, and Boltzmann distribution functions, and simple models for metals, semiconductors, and devices such as electron microscopes, scanning tunneling microscope, thermonic emitters, atomic force microscope, and others.

Subjects

applied quantum physics | applied quantum physics | quantum physics | quantum physics | statistical physics | statistical physics | quantum mechanics | quantum mechanics | Schrodinger | Schrodinger | tunneling | tunneling | harmonic oscillator | harmonic oscillator | hydrogen atom | hydrogen atom | variational methods | variational methods | Fermi-Dirac | Fermi-Dirac | Bose-Einstein | Bose-Einstein | Boltzmann | Boltzmann | distribution function | distribution function | electron microscope | electron microscope | scanning tunneling microscope | scanning tunneling microscope | thermonic emitter | thermonic emitter | atomic force microscope | atomic force microscope

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Quantum mechanics--even in the ordinary, non-relativistic, "particle" formulation that will be the primary focus of this course--has been a staggeringly successful physical theory, surely one of the crowning achievements of 20th century science. It's also rather bizarre--bizarre enough to lead very intelligent and otherwise sensible people to make such claims as that the universe is perpetually splitting into many copies of itself, that conscious minds have the power to make physical systems "jump" in unpredictable ways, that classical logic stands in need of fundamental revision, and much, much more. In this course, we intelligent and sensible people will attempt to take a sober look at these and other alleged implications of quantum mechanics, as well as certain stub Quantum mechanics--even in the ordinary, non-relativistic, "particle" formulation that will be the primary focus of this course--has been a staggeringly successful physical theory, surely one of the crowning achievements of 20th century science. It's also rather bizarre--bizarre enough to lead very intelligent and otherwise sensible people to make such claims as that the universe is perpetually splitting into many copies of itself, that conscious minds have the power to make physical systems "jump" in unpredictable ways, that classical logic stands in need of fundamental revision, and much, much more. In this course, we intelligent and sensible people will attempt to take a sober look at these and other alleged implications of quantum mechanics, as well as certain stub

Subjects

relativity | relativity | particle | particle | approximation technique | approximation technique | scientific inquiry | scientific inquiry | experiment | experiment | observation | observation | quantum theory | quantum theory | quantum mechanics | quantum mechanics

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This course, along with the next course in this sequence (8.06, Quantum Physics III) in a two-course sequence covering quantum physics with applications drawn from modern physics. General formalism of quantum mechanics: states, operators, Dirac notation, representations, measurement theory. Harmonic oscillator: operator algebra, states. Quantum mechanics in three-dimensions: central potentials and the radial equation, bound and scattering states, qualitative analysis of wavefunctions. Angular momentum: operators, commutator algebra, eigenvalues and eigenstates, spherical harmonics. Spin: Stern-Gerlach devices and measurements, nuclear magnetic resonance, spin and statistics. Addition of angular momentum: Clebsch-Gordan series and coefficients, spin systems, and allotropic forms of hydrogen This course, along with the next course in this sequence (8.06, Quantum Physics III) in a two-course sequence covering quantum physics with applications drawn from modern physics. General formalism of quantum mechanics: states, operators, Dirac notation, representations, measurement theory. Harmonic oscillator: operator algebra, states. Quantum mechanics in three-dimensions: central potentials and the radial equation, bound and scattering states, qualitative analysis of wavefunctions. Angular momentum: operators, commutator algebra, eigenvalues and eigenstates, spherical harmonics. Spin: Stern-Gerlach devices and measurements, nuclear magnetic resonance, spin and statistics. Addition of angular momentum: Clebsch-Gordan series and coefficients, spin systems, and allotropic forms of hydrogen

Subjects

General formalism of quantum mechanics: states | General formalism of quantum mechanics: states | operators | operators | Dirac notation | Dirac notation | representations | representations | measurement theory | measurement theory | Harmonic oscillator: operator algebra | Harmonic oscillator: operator algebra | states | states | Quantum mechanics in three-dimensions: central potentials and the radial equation | Quantum mechanics in three-dimensions: central potentials and the radial equation | bound and scattering states | bound and scattering states | qualitative analysis of wavefunctions | qualitative analysis of wavefunctions | Angular momentum: operators | Angular momentum: operators | commutator algebra | commutator algebra | eigenvalues and eigenstates | eigenvalues and eigenstates | spherical harmonics | spherical harmonics | Spin: Stern-Gerlach devices and measurements | Spin: Stern-Gerlach devices and measurements | nuclear magnetic resonance | nuclear magnetic resonance | spin and statistics | spin and statistics | Addition of angular momentum: Clebsch-Gordan series and coefficients | Addition of angular momentum: Clebsch-Gordan series and coefficients | spin systems | spin systems | allotropic forms of hydrogen | allotropic forms of hydrogen | Angular momentum | Angular momentum | Harmonic oscillator | Harmonic oscillator | operator algebra | operator algebra | Spin | Spin | Stern-Gerlach devices and measurements | Stern-Gerlach devices and measurements | central potentials and the radial equation | central potentials and the radial equation | Clebsch-Gordan series and coefficients | Clebsch-Gordan series and coefficients | quantum physics | quantum physics

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Introduction to the main concepts of string theory to undergraduates. Since string theory is quantum mechanics of a relativistic string, the foundations of the subject can be explained to students exposed to both special relativity (8.033) and basic quantum mechanics (8.05). Subject develops the aspects of string theory and makes it accessible to students familiar with basic electromagnetism (8.02) and statistical mechanics (8.044). This includes the study of D-branes and string thermodynamics. Introduction to the main concepts of string theory to undergraduates. Since string theory is quantum mechanics of a relativistic string, the foundations of the subject can be explained to students exposed to both special relativity (8.033) and basic quantum mechanics (8.05). Subject develops the aspects of string theory and makes it accessible to students familiar with basic electromagnetism (8.02) and statistical mechanics (8.044). This includes the study of D-branes and string thermodynamics.

Subjects

string theory | string theory | quantum mechanics | quantum mechanics | relativistic string | relativistic string | special relativity | special relativity | electromagnetism | electromagnetism | statistical mechanics | statistical mechanics | D-branes | D-branes | string thermodynamics | string thermodynamics | Light-cone | Light-cone | Tachyons | Tachyons | Kalb-Ramond fields | Kalb-Ramond fields | Lorentz invariance | Lorentz invariance | Born-Infeld electrodynamics | Born-Infeld electrodynamics | Hagedorn temperature | Hagedorn temperature | Riemann surfaces | Riemann surfaces | fermionic string theories | fermionic string theories | nuclear reactions | nuclear reactions

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This subject describes the fundamentals of bonding, energetics, and structure that underpin materials science. From electrons to silicon to DNA: the role of electronic bonding in determining the energy, structure, and stability of materials. Quantum mechanical descriptions of interacting electrons and atoms. Symmetry properties of molecules and solids. Structure of complex and disordered materials. Introduction to thermodynamic functions and laws governing equilibrium properties, relating macroscopic behavior to molecular models of materials. Develops basis for understanding a broad range of materials phenomena, from heat capacities, phase transformations, and multiphase equilibria to chemical reactions and magnetism. Fundamentals are taught using real-world examples such as engineered all This subject describes the fundamentals of bonding, energetics, and structure that underpin materials science. From electrons to silicon to DNA: the role of electronic bonding in determining the energy, structure, and stability of materials. Quantum mechanical descriptions of interacting electrons and atoms. Symmetry properties of molecules and solids. Structure of complex and disordered materials. Introduction to thermodynamic functions and laws governing equilibrium properties, relating macroscopic behavior to molecular models of materials. Develops basis for understanding a broad range of materials phenomena, from heat capacities, phase transformations, and multiphase equilibria to chemical reactions and magnetism. Fundamentals are taught using real-world examples such as engineered all

Subjects

fundamentals of bonding | energetics | and structure | fundamentals of bonding | energetics | and structure | Quantum mechanical descriptions of interacting electrons and atoms | Quantum mechanical descriptions of interacting electrons and atoms | Symmetry properties of molecules and solids | Symmetry properties of molecules and solids | complex and disordered materials | complex and disordered materials | thermodynamic functions | thermodynamic functions | equilibrium properties | equilibrium properties | macroscopic behavior | macroscopic behavior | molecular models | molecular models | heat capacities | heat capacities | phase transformations | phase transformations | multiphase equilibria | multiphase equilibria | chemical reactions | chemical reactions | magnetism | magnetism | engineered alloys | engineered alloys | electronic and magnetic materials | electronic and magnetic materials | ionic and network solids | ionic and network solids | polymers | polymers | biomaterials | biomaterials | energetics | energetics | structure | structure | materials science | materials science | electrons | electrons | silicon | silicon | DNA | DNA | electronic bonding | electronic bonding | energy | energy | stability | stability | quantum mechanics | quantum mechanics | atoms | atoms | interactions | interactions | symmetry | symmetry | molecules | molecules | solids | solids | complex material | complex material | disorderd materials | disorderd materials | thermodynamic laws | thermodynamic laws | electronic materials | electronic materials | magnetic materials | magnetic materials | ionic solids | ionic solids | network solids | network solids | statistical mechanics | statistical mechanics | microstates | microstates | microscopic complexity | microscopic complexity | entropy | entropy

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This class will study some of the changing ideas within modern physics, ranging from relativity theory and quantum mechanics to solid-state physics, nuclear and elementary particles, and cosmology. These ideas will be situated within shifting institutional, cultural, and political contexts. The overall aim is to understand the changing roles of physics and of physicists over the course of the twentieth century. This class will study some of the changing ideas within modern physics, ranging from relativity theory and quantum mechanics to solid-state physics, nuclear and elementary particles, and cosmology. These ideas will be situated within shifting institutional, cultural, and political contexts. The overall aim is to understand the changing roles of physics and of physicists over the course of the twentieth century.

Subjects

relativity theory | relativity theory | quantum mechanics | quantum mechanics | solid-state physics | solid-state physics | elementary particles | elementary particles | quarks | quarks | cosmology | cosmology | nuclear weapons | nuclear weapons | Maxwell | Maxwell | Mach | Mach | Bohr | Bohr | Heisenberg | Heisenberg | McCarthyism | McCarthyism | Poincar? | Poincar? | Schr?dinger | Schr?dinger | nuclear particles | nuclear particles | physics | physics | 20th century | 20th century | twentieth century | twentieth century | physicists | physicists | institutional | political | cultural context | institutional | political | cultural context | STS.042 | STS.042 | 8.225 | 8.225

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Includes audio/video content: AV special element video. This course discusses applications of electromagnetic and equivalent quantum mechanical principles to classical and modern devices. It covers energy conversion and power flow in both macroscopic and quantum-scale electrical and electromechanical systems, including electric motors and generators, electric circuit elements, quantum tunneling structures and instruments. It studies photons as waves and particles and their interaction with matter in optoelectronic devices, including solar cells, displays, and lasers. The instructors would like to thank Scott Bradley, David Friend, Ta-Ming Shih, and Yasuhiro Shirasaki for helping to develop the course, and Kyle Hounsell, Ethan Koether, and Dmitri Megretski for their work preparing the lect Includes audio/video content: AV special element video. This course discusses applications of electromagnetic and equivalent quantum mechanical principles to classical and modern devices. It covers energy conversion and power flow in both macroscopic and quantum-scale electrical and electromechanical systems, including electric motors and generators, electric circuit elements, quantum tunneling structures and instruments. It studies photons as waves and particles and their interaction with matter in optoelectronic devices, including solar cells, displays, and lasers. The instructors would like to thank Scott Bradley, David Friend, Ta-Ming Shih, and Yasuhiro Shirasaki for helping to develop the course, and Kyle Hounsell, Ethan Koether, and Dmitri Megretski for their work preparing the lect

Subjects

electromagnetics | electromagnetics | quantum mechanics | quantum mechanics | energy conversion | energy conversion | power flow | power flow | electric motors | electric motors | circuits | circuits | quantum tunneling | quantum tunneling | optoelectronic devices | optoelectronic devices | electromagnetic waves | electromagnetic waves | EM waves | EM waves | semiconductors | semiconductors | lasers | lasers

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