Quantum Mechanics

Instructor:    張明哲 
Textbook:   Principles of Quantum Mechanics, by R. Shankar
References: Modern Quantum Mechanics, by J.J. Sakurai; 量子力學, 曾謹嚴著
Grading:      homework (20%); mid-term exam (40%), final exam (40%)
Teaching Assistant: 黃超群

Order of presentation (actual presentation mixes Shankar with Sakurai)

First semester
    Chap 1 Mathematical introduction << important!
                A brief review of vector space, matrices, and operators
    Chap 2 Review of classical Mechanics (skip)
    Chap 3 All is not well with classical mechanics
    Chap 4 The postulates << important!
                Basic postulates of quantum mechanics 
                Spin system (the simplest quantum system) as an example
    Chap 9 The Heisenberg uncertainty relations
                The basic limit on the precision of physical measurement
    Chap 5 Simple problems in one dimension
                A brief review of one-dimensional systems
    Chap 6 The classical limit (skip)
    Chap 7 The harmonic oscillator
                Introducing creation/annihilation operators
    Chap 8 Path integral formulation of quantum theory
                Introducing Feynman's important work    
    Chap10 Systems with N degrees of freedom
                A brief introduction to many-body systems
    Chap11 Symmetries and their consequences

Second semester

    Chap 11 Symmetries and their consequences

                  Space translation, time evolution, parity transformation

    Chap 12 Rotation invariance and angular momentum

                  Angular momentum operator L

                  Eigenvalues and eigenfunctions of angular momentum

                  Unitary operator for  finite-rotation

    Chap 13 The hydrogen atom (skip)

    Chap 14 Spin

                  Two-component spinor

                  Rotation of spinor

                  Dynamics of spinor, ESR

    Chap 15 Addition of angular momentum

                  Addition of spins

                  Addition of orbital angular momentum and spin

                  Clebsch-Gordon coefficient

    Chap 16 The variational and WKB methods

                  The variational method (skip)

                  The WKB approximation

    Chap 17 Time-independent perturbation theory

                  Non-degenerate case

                  Degenerate case

    Chap 18 Time-dependent perturbation theory

                  Sudden perturbation

                  Adiabatic perturbation,  the Berry phase

                  Periodic perturbation

    Chap 19 Scattering theory

                  The Born approximation

                  Method of partial waves

                  Inelastic scattering

    Summer vacation!