量子力学 2010-2011秋季学期 2008级数理科学

任课老师

Quantum Mechanics

 

Xiao-Gang He

 

Reference books:

 

量子力学 I 曾谨言 第四版

量子力学, 蔡建华

量子力学,苏汝铿

Modern Quantum Mechanics, J.J. Sakurai

Principles of Quantum Mechanics, R. Shankar

Introductory Quantum Mechanics, Richard L. Liboff

 

Outline

 

1.      A Brief History of Quantum Mechanics

Blackbody radiation; Photoelectric effect; Stability and spectrum of atom; Bohr model; Correspondence principle; de Broglie matter wave; Superposition principle; Schrodinger equation.

 

2.      The Postulates of Quantum Mechanics

State of vector; Observable and Measurement; Schrodinger equation; Superposition principle and Schrodinger equation; Schrodinger equation in three dimensions; Uncertainty principle; Continuity equation of probability; Classic Limit, Dirac Notation.

 

3.      Simple Quantum Mechanics Problems

A Free particle; A particle in a box; The step and delta potential problems; Some theorems; Energy levels in periodic potential; The harmonic oscillator.

 

4.      Solving the three dimensional Schrodinger Equation

Separation of variable method; Rectangular coordinate; Spherical Coordinate; Orbital angular momentum; Free particle in spherical coordinate; Hydrogen atom; Cylindrical coordinate.

 

5.      System with N degrees of Freedom

N particle system; The Hilbert space; Identical particles.

 

6.      Symmetries and Their Consequences

Symmetries and conservation laws; Time and space translational symmetries; Parity and Time-reversal Symmetries; Rotational symmetry; Angular momentum again.

 

7.      Charged particle in quantum mechanics

Schrodinger equation in electromagnetic field; The Aharonov-Bohm effect; Charged particle in magnetic field and Landau level; Zeeman effect.

 

8.      Spin in Quantum Mechanics

Anomalous Zeeman effect and spin; Kinematics of spin; Spin dynamics; Addition of angular momentum; Entangled states; Spin-orbital interaction; Multi-electron atoms and the periodic Table..

 

9.      Approximate Methods in Quantum Mechanics

Variational method; WKB method; Time-independent and time-dependent perturbation methods; Fermi’s Golden rule; Other example calculations.

 

10.  Scattering Theory

Scattering cross section and Quantum mechanics; Born approximation for scattering amplitude; Partial wave analysis; Scattering of identical particles.

 

11.  Dirac eqution

Diract equation; Diract eqution for a charged particle; Magnetic dipole interaction; Spin-orbital interaction; Plane wave solution.

 

Final grade

 

30% on homework and 70% on middle and final exams.