Phy5645
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 for 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
Chapter 7: Angular Momentum
Commutation relations Angular momentum as a generator of rotations in 3D Spherical Coordinates Eigenvalue quantization Orbital angular momentum eigenfunctions Problems on Angular Momentum
Chapter 8: Central Forces
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