Phy5645
Welcome to the Quantum Mechanics A PHY5645 Fall2008/2009
The most fundamental equation of quantum mechanics; given a Hamiltonian , it describes how a state evolves in time.
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
- Brief Derivation of Schrödinger Equation
- Relation Between the Wave Function and Probability Density
- Stationary States
- Heisenberg Uncertainty Principle
- Some Consequences of the Uncertainty Principle
Chapter 3: Operators, Eigenfunctions, and Symmetry
- Linear Vector Spaces and Operators
- Commutation Relations and Simultaneous Eigenvalues
- The Schrödinger Equation in Dirac Notation
- Transformations of Operators and Symmetry
- Time Evolution of Expectation Values and Ehrenfest's Theorem
Chapter 4: Motion in One Dimension
- One-Dimensional Bound States
- Oscillation Theorem
- The Dirac Delta Function Potential
- Scattering States, Transmission and Reflection
- Motion in a Periodic Potential
- Summary of One-Dimensional Systems
Chapter 5: Discrete Eigenvalues and Bound States - The Harmonic Oscillator and the WKB Approximation
- Harmonic Oscillator Spectrum and Eigenstates
- Analytical Method for Solving the Simple Harmonic Oscillator
- Coherent States
- Charged Particles in an Electromagnetic Field
- WKB Approximation
Chapter 6: Time Evolution and the Pictures of Quantum Mechanics
- The Heisenberg Picture: Equations of Motion for Operators
- The Interaction Picture
- The Virial Theorem
Chapter 7: Angular Momentum
- Commutation Relations
- Angular Momentum as a Generator of Rotations in 3D
- Spherical Coordinates
- Eigenvalue Quantization
- Orbital Angular Momentum Eigenfunctions
Chapter 8: Central Forces
- General Formalism
- Free Particle in Spherical Coordinates
- Spherical Well
- Isotropic Harmonic Oscillator
- Hydrogen Atom
- WKB in Spherical Coordinates
Chapter 9: The Path Integral Formulation of Quantum Mechanics
Chapter 10: Continuous Eigenvalues and Collision Theory