量子力学 I， 曾谨言 第四版
Modern Quantum Mechanics, J.J. Sakurai
Principles of Quantum Mechanics, R. Shankar
Introductory Quantum Mechanics, Richard L. Liboff
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.
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