Phys622: (Spring 2008)
Quantum Mechanics II

Course calendar:

There is a brief description of the content for each lecture, together with links to handouts (HW, etc). The references (in red) point to parts in the text and reference books that may be helpful in complementing your lecture notes.
Th 1/17
  • General information.

  • SG experiment 
        -  Sakurai 1.1  
        -  Aneasy-reading on-line intro on the SG.

    -- Homework Assignment 0 (pdf file) out.

    • Tu 1/22
  • Schrodinger Equation and wave functions 
        -  Lecture notes; Sakurai 1.3
  • Introduction Dirac notation; connection with wave mechanics. 
        -  Sakurai 1.2
    • Th 1/24 No classes --- I am teaching at a winter school being held at the International Center for Theoretical Physics in Trieste, Italy.
    Tu 1/29
    Th 1/31
    Tu 2/5
  • Dirac notation 
        -  Sakurai 1.2
    -- Homework Assignment 1 out.
    • Th 2/7
  • Base kets and matrix representation 
        -  Sakurai 1.3
  • Measurements and observables 
        -  Sakurai 1.4
    • Tu 2/12
  • Spin 1/2 systems -- formal development. 
        -  Sakurai 1.3, 1.4
  • Compatible and incompatible observables. 
        -  Sakurai 1.4
  • The uncertainty relation 
        -  Sakurai 1.4
    • Th 2/14
  • The uncertainty relation, cont'd 
        -  Sakurai 1.4
  • Change of basis 
        -  Sakurai 1.5
  • Additional Reading: Diagonalization and Unitary equivalent operators 
        -  Sakurai 1.5
    -- Homework Assignment 2 out.
    • Tu 2/19
  • Position basis and wave function, revisited 
        -  Sakurai 1.6, 1.7
  • Translation and momentum. 
        -  lecture notes; Sakurai 1.6
  • Wave functions. 
        -  Sakurai 1.7, including Gaussian wave packets
    • Th 2/21
  • Time evolution operator. 
        -  Sakurai 2.1
  • Introduction to quantum dynamics. 
        -  Sakurai 2.1
    		•
    Tu 2/26
  • Quantum dynamics. 
        -  Sakurai 2.1; lecture notes
  • The Schrodinger equation 
        -  Sakurai 2.4
  • Axioms of quantum theory 
        -  Lecture notes
    -- Homework Assignment 3 out.
    • Th 2/28
  • Heisenberg picture, Ehrenfest's theorem. 
        -  Sakurai 2.2
  • Propagators; introduction to path integrals. 
        -  Sakurai 2.5; lecture notes
    • Tu 3/4 Have a great Spring Break!
    Th 3/6
    Tu 3/11
  • Propagators and Path integrals. 
        -  Sakurai 2.5; lecture notes
  • Additional Reading for this week: Algebraic method applied to the Simple Harmonic oscillator 
        -  Sakurai 2.3
    • Th 3/13
  • Path integrals, cont'd. 
        -  Sakurai 2.5; lecture notes
  • Electron in a magnetic field 
        -  Sakurai 2.6
    -- Homework Assignment 4 out.

    • Tu 3/18
  • Electron in a magnetic field, gauge transformations 
        -  Sakurai 2.6
    • Th 3/20 No class today
    Tu 3/25
  • Flux quantization. 
        -  lecture notes; Prob 2.25
  • The Aharonov-Bohm effect 
        -  Sakurai 2.6
  • Symmetry: Parity 
        - Sakurai Sec. 4.2; lecture notes
    • We 3/26 Make-up class: problem session covering hw0-4; Q/A (10am-12pm in Physics conference room)
    Th 3/27
  • Lattice translation symmetry, Bloch's theorem 
        -  lecture notes; Sakurai Sec. 4.3
  • The Kronig-Penney model --- metals and insulators 
        -  lecture notes
    -- take-home midterm out
    • Tu 4/1
  • The time-reversal symmetry 
        -  Sakurai Sec. 4.4
  • Permutation symmetry (of identical particles) 
        -  Sakurai Sec. 6.1; lecture notes
    -- Homework Assignment 5 out.
    • Th 4/3
  • Many-Boson and many-Fermion systems 
        -  lecture notes; Sakurai Sec's 6.2, 6.3
    		•
    Tu 4/8
  • Pauli's exclusion principle 
        -  lecture notes; Sakurai Sec. 6.3
  • many-electron systems --- Fermi energy and Fermi momentum 
        -  lecture notes
  • Reading: mixed symmetry, Young Tableaux and applications 
        -  Sakurai Sec. 6.3; Sec. 6.5.
    • Th 4/10
  • e-e interactions and the Helium atom 
        -  lecture notes; Sakurai Sec. 6.4
  • Reading: review stationary perturbation theory (covered last semester) 
        -  Sakurai Sec.'s 5.1, 5.2.
  • Stark effect in hydrogen (n=1 and n=2) 
        -  Sakurai Sec. 5.2; lecture notes
    -- Homework Assignment 6 out.
    • Tu 4/15
  • Stark effect in hydrogen, cont'd. 
        -  Sakurai Sec. 5.2; lecture notes
  • Additional Reading: The Zeeman effect 
        -  Sakurai 5.3
  • Intro to time-dependent perturbation theory. 
        -  Sakurai sec.'s 5.5, 5.6, 7.11
    • Th 4/17
  • Transition amplitudes and probabilities 
        -  Sakurai sec. 5.6
    • Tu 4/22
  • Fermi's golden rule. 
        -  Sakurai sec.'s 5.6 and 5.8
  • The time-independent formulation -- Lippmann-Schwinger eq. 
        -  Sakurai 7.1
  • Born series and Born approximation 
        -  Sakurai 7.2; lecture notes
    • Th 4/24
  • Intro. to scattering theory 
        -  Sakurai 7.1
  • Additional Reading: Partial wave method 
        -  Sakurai 7.6
  • Summary

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