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<b>[[Physical Basis of Quantum Mechanics|Chapter 1: Physical Basis of Quantum Mechanics]]</b> | <b>[[Physical Basis of Quantum Mechanics|Chapter 1: Physical Basis of Quantum Mechanics]]</b> | ||
Basic Concepts and Theory of Motion | * Basic Concepts and Theory of Motion | ||
UV Catastrophe (Black Body Radiation) | * UV Catastrophe (Black Body Radiation) | ||
Photoelectric Effect | * Photoelectric Effect | ||
Stability of Matter | * Stability of Matter | ||
Double Slit Experiment | * Double Slit Experiment | ||
Stern-Gerlach Experiment | * Stern-Gerlach Experiment | ||
The principle of complementarity | * The principle of complementarity | ||
The Correspondence Principle | * The Correspondence Principle | ||
The Philosophy of Quantum Theory | * The Philosophy of Quantum Theory | ||
<b>[[Schrödinger equation|Chapter 2: Schrödinger Equation]]</b> | <b>[[Schrödinger equation|Chapter 2: Schrödinger Equation]]</b> | ||
Original Idea of Schrödinger Equation | * Original Idea of Schrödinger Equation | ||
Brief deviation of Schrodinger Equation | * Brief deviation of Schrodinger Equation | ||
Stationary states | * Stationary states | ||
Conservation of probability | * Conservation of probability | ||
States, Dirac bra-ket notation | * States, Dirac bra-ket notation | ||
Heisenberg Uncertainty relations | * Heisenberg Uncertainty relations | ||
Some Consequences of the Uncertainty Principle | * Some Consequences of the Uncertainty Principle | ||
<b>[[Motion in one dimension|Chapter 3: Motion in One Dimension]]</b> | <b>[[Motion in one dimension|Chapter 3: Motion in One Dimension]]</b> | ||
1D bound states | * 1D bound states | ||
The Dirac Delta function potential | * The Dirac Delta function potential | ||
Scattering states | * Scattering states | ||
Oscillation theorem | * Oscillation theorem | ||
Transmission-Reflection, S-matrix | * Transmission-Reflection, S-matrix | ||
Motion in a periodic potential | * Motion in a periodic potential | ||
Summary of 1D Systems | * Summary of 1D Systems | ||
<b>[[Operators, eigenfunctions, symmetry, and time evolution|Chapter 4: Operators, Eigenfunctions, Symmetry, and Time Evolution]]</b> | <b>[[Operators, eigenfunctions, symmetry, and time evolution|Chapter 4: Operators, Eigenfunctions, Symmetry, and Time Evolution]]</b> | ||
Linear Vector Space and Operators | * Linear Vector Space and Operators | ||
Commutation relations and simultaneous eigenvalues | * Commutation relations and simultaneous eigenvalues | ||
Symmetry and Its Role in Quantum Mechanics | * Symmetry and Its Role in Quantum Mechanics | ||
Ehrenfest's Theorem | * Ehrenfest's Theorem | ||
Heisenberg and interaction picture: Equations of motion for operators | * Heisenberg and interaction picture: Equations of motion for operators | ||
The Interaction Picture | * The Interaction Picture | ||
The Virial Theorem | * The Virial Theorem | ||
Feynman path integrals | * Feynman path integrals | ||
Problems | * Problems | ||
<b>[[Discrete_eigenvalues_and_bound_states._Harmonic_oscillator_and_WKB_approximation|Chapter 5: Discrete Eigenvalues and Bound States]]</b> | <b>[[Discrete_eigenvalues_and_bound_states._Harmonic_oscillator_and_WKB_approximation|Chapter 5: Discrete Eigenvalues and Bound States]]</b> | ||
Harmonic oscillator spectrum and eigenstates | * Harmonic oscillator spectrum and eigenstates | ||
Analytical Method for Solving the Simple Harmonic Oscillator | * Analytical Method for Solving the Simple Harmonic Oscillator | ||
Coherent states | * Coherent states | ||
Feynman path integral evaluation of the propagator | * Feynman path integral evaluation of the propagator | ||
<b>[[Path Integral Evaluation of the Free-Particle Propagator|Chapter 6: Path Integral Evaluation of the Free-Particle Propagator]]</b> | <b>[[Path Integral Evaluation of the Free-Particle Propagator|Chapter 6: Path Integral Evaluation of the Free-Particle Propagator]]</b> | ||
Saddle point action | * Saddle point action | ||
Harmonic fluctuations | * Harmonic fluctuations | ||
Motion in electromagnetic field | * Motion in electromagnetic field | ||
WKB Approximation | * WKB Approximation | ||
<b>[[Angular momentum|Chapter 7: Angular Momentum]]</b> | <b>[[Angular momentum|Chapter 7: Angular Momentum]]</b> | ||
Commutation relations | * Commutation relations | ||
Angular momentum as a generator of rotations in 3D | * Angular momentum as a generator of rotations in 3D | ||
Spherical Coordinates | * Spherical Coordinates | ||
Eigenvalue quantization | * Eigenvalue quantization | ||
Orbital angular momentum eigenfunctions | * Orbital angular momentum eigenfunctions | ||
Problems on Angular Momentum | * Problems on Angular Momentum | ||
<b>[[Central forces|Chapter 8: Central Forces]]</b> | <b>[[Central forces|Chapter 8: Central Forces]]</b> | ||
Generalized derivation | * Generalized derivation | ||
Free particle in spherical coordinates | * Free particle in spherical coordinates | ||
Spherical well | * Spherical well | ||
Isotropic Harmonic Oscillator | * Isotropic Harmonic Oscillator | ||
Hydrogen atom | * Hydrogen atom | ||
WKB in spherical coordinates | * WKB in spherical coordinates | ||
<b>[[Continuous eigenvalues and collision theory|Chapter 9: Continuous Eigenvalues and Collision Theory]]</b> | <b>[[Continuous eigenvalues and collision theory|Chapter 9: Continuous Eigenvalues and Collision Theory]]</b> | ||
Differential cross-section and the Green's function formulation of scattering | * Differential cross-section and the Green's function formulation of scattering | ||
Central potential scattering and phase shifts | * Central potential scattering and phase shifts | ||
Born approximation and examples of cross-section calculations | * Born approximation and examples of cross-section calculations | ||
Coulomb potential scattering | * Coulomb potential scattering | ||
Two particle scattering | * Two particle scattering | ||
Revision as of 16:25, 29 January 2013
Welcome to the Quantum Mechanics A PHY5645 Fall2008/2009
This is the first semester of a two-semester graduate level sequence, the second being PHY5646 Quantum B. Its goal is to explain the concepts and mathematical methods of Quantum Mechanics, and to prepare a student to solve quantum mechanics problems arising in different physical applications. The emphasis of the courses is equally on conceptual grasp of the subject as well as on problem solving. This sequence of courses builds the foundation for more advanced courses and graduate research in experimental or theoretical physics.
The key component of the course is the collaborative student contribution to the course Wiki-textbook. Each team of students is responsible for BOTH writing the assigned chapter AND editing chapters of others.
Team assignments: Fall 2009 student teams
Fall 2009 Midterm is October 15
Outline of the course:
Chapter 1: Physical Basis of Quantum Mechanics
- Basic Concepts and Theory of Motion
- UV Catastrophe (Black Body Radiation)
- Photoelectric Effect
- Stability of Matter
- Double Slit Experiment
- Stern-Gerlach Experiment
- The principle of complementarity
- The Correspondence Principle
- The Philosophy of Quantum Theory
Chapter 2: Schrödinger Equation
- Original Idea of Schrödinger Equation
- Brief deviation of Schrodinger Equation
- Stationary states
- Conservation of probability
- States, Dirac bra-ket notation
- Heisenberg Uncertainty relations
- Some Consequences of the Uncertainty Principle
Chapter 3: Motion in One Dimension
- 1D bound states
- The Dirac Delta function potential
- Scattering states
- Oscillation theorem
- Transmission-Reflection, S-matrix
- Motion in a periodic potential
- Summary of 1D Systems
Chapter 4: Operators, Eigenfunctions, Symmetry, and Time Evolution
- Linear Vector Space and Operators
- Commutation relations and simultaneous eigenvalues
- Symmetry and Its Role in Quantum Mechanics
- Ehrenfest's Theorem
- Heisenberg and interaction picture: Equations of motion for operators
- The Interaction Picture
- The Virial Theorem
- Feynman path integrals
- Problems
Chapter 5: Discrete Eigenvalues and Bound States
- Harmonic oscillator spectrum and eigenstates
- Analytical Method for Solving the Simple Harmonic Oscillator
- Coherent states
- Feynman path integral evaluation of the propagator
Chapter 6: Path Integral Evaluation of the Free-Particle Propagator
- Saddle point action
- Harmonic fluctuations
- Motion in electromagnetic field
- WKB Approximation
- Commutation relations
- Angular momentum as a generator of rotations in 3D
- Spherical Coordinates
- Eigenvalue quantization
- Orbital angular momentum eigenfunctions
- Problems on Angular Momentum
- Generalized derivation
- Free particle in spherical coordinates
- Spherical well
- Isotropic Harmonic Oscillator
- Hydrogen atom
- WKB in spherical coordinates
Chapter 9: Continuous Eigenvalues and Collision Theory
- Differential cross-section and the Green's function formulation of scattering
- Central potential scattering and phase shifts
- Born approximation and examples of cross-section calculations
- Coulomb potential scattering
- Two particle scattering