Fall 2019

Physics 570A: Quantum Mechanics

 

    Course information

    Textbook:
    R. Shankar, Principles of Quantum Mechanics (2nd Edition, Springer, 2008).

    Learning Objectives
    Axiomatic theory of quantum mechanics (state vectors, operators, Hilbert space, measurement theory); the uncertainty principle; position, momentum, and linear translations; time evolution and quantum dynamics; wave equation for a particle in a classical electromagnetic field; harmonic oscillators; path-integral formulation of quantum mechanics; theory of rotations and angular momentum; density matrix and quantum ensembles; addition of angular momentum.

    Office hours: Wednesday, 2-4pm, or contact me

    Grades available on d2l

    Homework (due in class):
    HW1 due 9/5: Shankar 1.1.3, 1.1.4, 1.3.4, 1.6.2, 1.6.3, 1.8.5, 1.8.10, 1.9.1
    HW2 due 9/12: Shankar 1.10.1, 1.10.2, 1.10.3, 4.2.1, 4.2.2, 5.3.1, 5.3.4
    HW3 due 9/19

    Solutions:
    HW1 HW2

    Lecture notes: (under construction!)
    Lec 1: Chronology of Quantum Mechanics
    Lec 2: Uncertainty principle
    2-Slit Gedankenexperiment (Feynman lectures III.1)
    Experiment with an Atom Interferometer
    Lec 3: Wave mechanics
    Lec 4: The postulates of QM
    Lec 5: The state vector; bras and kets
    Lec 6: Inner products and operators
    Lec 7: Proofs of uncertainty principle, Ehrenfest's theorem
    Lec 8: Parity and translation
    Lec 9: Operator equations of motion
    Lec 10: Energy-time uncertainty relation
    Lec 11: 1D scattering
    Lec 12: Resonant tunneling
    Lec 13: Harmonic oscillator
    Lec 13b: Oscillator matrix elements
    Lec 14: Meissner effect
    Lec 15: Aharonov-Bohm effect
    Lec 16: Feynman path integral approach
    Lec 17: Angular momentum operators
    Lec 18: Angular momentum matrices
    Lec 19: Angular momentum measurements
    Lec 20: Rotations
    Lec 21: Angular momentum wavefunctions
    Lec 22: The density matrix (includes bonus material)
    Lec 23: Addition of angular momenta

    Additional references:
    J. J. Sakurai and J. Napolitano, Modern Quantum Mechanics (2nd Edition, Pearson/Addison- Wesley, 2011).

    Leslie E. Ballentine, Quantum Mechanics: A Modern Development (World Scientific Publishing Company, 2000). Mathematical approach.

    Gordon Baym, Lectures on Quantum Mechanics (CRC Press, 2018). Informal but very good.

    Claude Cohen-Tannoudji, Bernard Diu, Franck Laloe Quantum Mechanics, Volumes 1-2 (Wiley, 2005). An encyclopedia of QM.

    David J. Griffiths, Introduction to Quantum Mechanics (2nd Edition, Pearson/Prentice Hall, 2005). Standard undergraduate text good for a review of the basics.

    Simulations of wave packet dynamics and 1D scattering (try it!)

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