March 9, 2000

QUANTUM MECHANICS
  

Physics D12-2   - Jan 6 to March 9 Winter Quarter 2000
TTh 2:30-4:00 in Tech F328 Predrag Cvitanovic'
Course schedule
quantum puppy
They are so cute when they try to understand Quantum Mechanics.

www.phys.nwu.edu/~predrag/NUcourses/D12-2-2000/index.html
NU Registrar course description
http://now.nwu.edu/registration/owa/

For people following the course, check the e-mail list.


PROBLEM SETS: Please deliver solutions to problem sets by Thursday, at the lecture, or place them in Yueheng Lan's Physics & Astronomy mailbox (y-lan@nwu.edu).


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  1. Feynman's Formulation of Quantum Mechanics
    1. Schrödinger's Wave Equation
    2. QM Amplitudes as a Sum over Paths
    3. Classical Limit
    Suggested reading:
    Predrag's lecture notes (postscript gzipped) -
    Chapter 1: Path Integrals
    Merzbacher: Sect 8.7 - The equation of Motion
    Merzbacher: Chapt 14 - Linear Vector Spaces
    Further (optional) reading:
    Brown: Chap 1 - Functional integrals (Very clear)
    R.P. Feynman and A.R. Hibbs: Chaps 1-3 (get it from the horse's mouth)
    Schulman: Chaps 1-3 (standard reference on QM path integrals)
    Exercises:
    Problem set 1, tex file, due January 20, 2000

  2. WKB approximation

  3. Suggested reading:
    Predrag's lecture notes (postscript gzipped) -
    Chapter 2: WKB approximation
    Merzbacher: chapter 7
    Further (optional) reading:
    Griffiths: chapter 8 (I like it better than Merzbacher version)

  4. Symmetry in QM
    1. Spherically symmetric potentials
    2. Angular momentum & rotational symmetry
    3. Spherical harmonics

    Suggested reading:
    Merzbacher: chapter 9
    Andrew Jackson: Quantum Mechanics explained
    Comments and supplementary topics on Liboff's text. [27 January 2000]
    Chapters 1 to 8: general stuff
    Chapters 9 to 12: central forces, angular momenta
    Predrag's lecture notes (postscript gzipped):
    Chapter 3: Discrete Fourier transform
    Appendix A: Group theory
    Exercises:
    Problem set 2: Merzbacher exercises 7.2, 7.3
    due February 8, 2000

    Exercises:
    Problem set 3: Angular momentum, - due February 17, 2000

  5. Wave Mechanics
    1. One- and two-body problems
    2. Coulomb field: hydrogen atom
    3. Angular momentum

    Suggested reading:
    Merzbacher: chapter 10

    Exercises:
    Problem set 4: Spherical well - due February 29, 2000

  6. Time independent perturbation theory
    1. Bound state perturbation theory
    2. Degenerate perturbation theory
    3. Zeeman & Stark effects

    Suggested reading:
    Merzbacher: chapter 17

    Exercises:
    Problem set 5: Time independent perturbation theory - due March 2, 2000

  7. Group theory for QM
    1. Linear momentum & translational symmetry
    2. Groups, representations, tensors, reducibility
    3. S0(3) rotational symmetry, and its representations

    Further, optional reading:
    (Read only for your own ediffication, not needed for any exams. This is a rather idiosyncratic presentation of the theory, I am curious to what extent you find it accessible)
    Predrag's draft manuscript (postscript gzipped):
    Chapter 1: Introduction
    Chapter 2: Preview
    Chapter 3: Invariants and irreducibility

  8. Perturbation theory applied to hydrogen
    1. Spin - orbit coupling
    2. Fine structure of hydrogen

    Suggested reading:
    Merzbacher: section 12.1, section 12.4, section 16.6 section 17.6
    A. Jackson: Chapters 9 to 12: central forces, angular momenta - pages 59-64, 77-86.

  9. Variational methods

  10. Suggested reading:
    Merzbacher: sections 8.9, 17.8, 17.9
    A. Jackson: Chapters 9 to 12: Helium - pages 92-94.


    Final exam Tuesday, 14 March 2000, 10:00-12:00.
      Syllabus for the final exam.

    Midterm exam mean score: 30 points out of 43 possible
    Scores: 6, 21, 24, 25, 28, 29, 31, 32, 32, 34, 35, 36.

    Problems sets mean score: 181 points out of 220 possible
    Scores: 202, 199, 194, 194, 193, 193, 192, 186, 179, 151, 145, 145.

    Overal course grade will be determined from the homework (40%), midterm (20%), and the final (40%).


    References

    1. Quantum Mechanics, E. Merzbacher (John Wiley, 1990).
    2. Quantum Mechanics and Path Integrals, R.P. Feynman and A.R. Hibbs (McGraw-Hill, New York 1965).
    3. Techniques and Applications of Path Integration, L.S. Schulman (Wiley, New York, 1981).
    4. Quantum Field Theory, L.S. Brown (Cambridge University Press, Cambridge 1992).
    5. Introduction to Quantum Mechanics, D.J. Griffiths (Prentice-Hall, Englewood Cliffs, New Jersey, 1994)
    6. Quantum Mechanics, 3 ed., Vol. 3, L. Landau & I. Lifshitz, Pergamon Press (1977).
    7. Lectures on Quantum Mechanics, G. Baym, Benjamin/Cummings Pub. Co. (1969).

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