Quantum Mechanics

Oberlin College Physics 312

Syllabus for Fall 2011

Teacher: Dan Styer, Wright 215, 775-8183, Dan.Styer@oberlin.edu
home telephone 440-281-1348 (2:30 pm to 9:00 pm only).

Office hours: Tuesday 2:30-3:30 pm, Friday 10:00-11:00 am, and by appointment.

Meeting times: Class: MWF at 11:00 am. Conference: Tuesday at 12:15 pm. Wright Laboratory room 114.

Course web site: http://www.oberlin.edu/physics/dstyer/QM.
I will post handouts, problem assignments, and model solutions here.

Textbooks:

Exams, homework, grading: There will be two in-semester exams and a final. All the exams will be two-hour open-book written take-home exams, and each will contribute 20% to your final grade. The in-semester exams will be due at 11:00 am on Wednesday 12 October and on Wednesday 16 November; the final exam will be due at 11:00 am on Saturday 17 December. Exams will cover topics from lectures and problem sets rather than from readings.

Problem assignments will be assigned each Wednesday, except for the Wednesdays preceding exams. Each is due in class the following Wednesday; late papers will be accepted only in cases of illness or family emergency. When writing your solutions, describe (in words) the thought that went into your work as well as describing (in equations) the mathematical manipulations involved. Your work on the problem assignments will contribute 40% to your final grade.

Anyone earning a final score of 50% or lower will not receive credit for this course.

Collaboration and references: I encourage you to collaborate or to seek printed help in working the problems, but the final write-up must be entirely your own: you may not copy word for word or equation for equation. When you do obtain outside help you must acknowledge it. (E.g. "By integrating Griffiths equation [8.5] I find that..." or "Employing the substitution u = sin(x) (suggested by Carol Hall)..." or even "In working these problems I benefited from discussions with Mike Fisher and Jim Newton.") Such an acknowledgement will never lower your grade; it is required as a simple matter of intellectual fairness.

Topics:

  1. The phenomena of quantum mechanics.
    Why do we need a quantum mechanics? The Stern-Gerlach experiment and two-state systems. Probability, interference, entanglement.
  2. Forging mathematical tools for quantum mechanics.
    What is a quantal state? State vectors, outer products, operators, and measurements -- all for two-state systems. Linear algebra. Formal properties ("postulates").
  3. Time evolution.
    The time development operator and the Schrödinger equation. Application to a two-state system: the ammonia maser. Formal properties of time evolution.
  4. Continuum systems.
    The Hamiltonian and momentum operators in one dimension. The classical limit (Ehrenfest's theorem). Motion of a free particle. Two nonidentical particles in one dimension -- configuration space.
  5. The infinite square well.
    Energy eigenstates. Time development.
  6. The simple harmonic oscillator.
    Energy eigenstates through differential equations and through operator factorization. Time development.
  7. Perturbation theory.
    Approximate solutions for the energy eigenproblem.
  8. Quantum mechanics in two and three dimensions.
  9. Angular momentum.
    Rotations and symmetries. Eigenproblem. Projections.
  10. Central force motion.
    Use of angular momentum. The Coulomb problem. Hydrogen atom fine structure.
  11. Identical particles.
  12. Return to conceptual foundations.
    Quantal motion as a sum over classical paths.

Quantum Mechanics Bibliography

You are of course free to disregard the assigned texts and use whatever reading materials you desire. Here are some books on reserve in the Science Center Library. (They are located on shelves along the south wall, not far to your right when you enter, near some comfy chairs to encourage browsing.)

Popular works:

D.F. Styer, The Strange World of Quantum Mechanics [Science QC174.12.S879 2000].
The calculational machinery of quantum mechanics is so magnificent and so formidable that it is easy to lose sight of what you're trying to calculate. This book works to keep the mathematics from obscuring the physics. (Tips for getting the most out of this book are at http://www.oberlin.edu/physics/dstyer/StrangeQM/.)

R.P. Feynman, QED: The Strange Theory of Light and Matter [Science QC793.5.P422F48 1985].
Another book, beautifully written, that emphasizes physics over mathematical technique. (Tips for getting the most out of this book are at http://www.oberlin.edu/physics/dstyer/TeachQM/QED.html.)

Undergraduate level texts:

D. McIntyre, C. Manogue, and J. Tate, Paradigms in Physics: Quantum Mechanics.
Soon to be published, but for now available at http://physics.oregonstate.edu/portfolioswiki/texts:quantumbook:start.

R. Shanker, Principles of Quantum Mechanics [Science QC174.12.S52 1994].
Nice discussions, conversational tone.

R.L. Liboff, Introductory Quantum Mechanics [Science QC174.12.L52 1991].
Has been used as the text for this course in the past.

R.G. Winter, Quantum Physics, second edition [Science QC174.12.W55 1986].
Another text previously used in this course.

R.W. Robinett, Quantum Mechanics: Classical Results, Modern Systems, and Visualized Examples [Science QC174.12.R6 2006].
A wonderful book, but not well-matched to this course. The author's resource page is at http://robinett.phys.psu.edu/qm/.

D. Park, Introduction to the Quantum Theory [Science QC174.12.P37 1974].
The old standard of undergraduate quantum mechanics texts.

Graduate level texts:

J.J. Sakurai, Modern Quantum Mechanics [Science QC174.12.S25 1985].

E. Merzbacher, Quantum Mechanics [Science QC174.1.M36 1970].

C. Cohen-Tannoudji, B. Diu, F. Laloë, Quantum Mechanics [Science QC174.12.C6313].
Do not drop. Includes many fascinating examples and applications usually bypassed in texts.

A. Messiah, Quantum Mechanics [Science QC174.1.M413].
Encyclopedic.

K. Gottfried, Quantum Mechanics [Science 530.12G713Q].
Unconventional. Don't look for volume two...it doesn't exist.

G. Baym, Lectures on Quantum Mechanics [Science 530.12B344L].
Avant-garde.

L.I. Schiff, Quantum Mechanics [Science 539.83Sch32Q.2].
The grand old man of graduate quantum mechanics texts. Based on Oppenheimer's lectures.

L.D. Landau and E.M. Lifshitz, Quantum Mechanics [Science 530.123L231Q].
So close to perfect that some think it is. It is not.

P.A.M. Dirac, The Principles of Quantum Mechanics, fourth edition [Science 539.83D627P.4].
The master's voice.

Books with a conceptual orientation:

A.P. French and E.F. Taylor, An Introduction to Quantum Physics, chapters 6 and 7 [Science QC174.12.F73].

T.F. Jordan, Quantum Mechanics in Simple Matrix Form [Science QC174.12.J67 1986].

R.P. Feynman, R.B. Leighton and M. Sands, The Feynman Lectures on Physics, volume 3 [Science oversized QC21.2.F49 2006 vol. 3].
Tips for getting the most out of this book are at http://www.feynmanlectures.info/.

R.P. Feynman and A.R. Hibbs, Quantum Mechanics and Path Integrals, chapter 1 [Science 530.12F438Q].
Tips for getting the most out of this book are at http://www.oberlin.edu/physics/dstyer/FeynmanHibbs/.

G. Greenstein and A. Zajonc, The Quantum Challenge: Modern Research on the Foundations of Quantum Mechanics [Science QC174.12.G73 2006].
Books on the foundations of quantum mechanics often wallow in vague philosophy. This one is full of crisp experiments.

Special topics:

D.T. Gillespie, A Quantum Mechanics Primer [Science 530.123G412Q].
An exceptionally clear treatment of the formalism of quantum mechanics.

J.R. Hiller, I.D. Johnston, and D.F. Styer, Quantum Mechanics Simulations [Science QC52.H55 1995].
Software and book.

J.S. Townsend, A Modern Approach to Quantum Mechanics [Science QC174.12.T69 1992].
Follows the sequence of topics used in this course (namely spin-1/2 first, followed by continuum systems), but its emphasis is formal rather than physical.

R.N. Zare, Angular Momentum: Understanding Spatial Aspects in Chemistry and Physics [Science QC793.3.A5 Z37 1988].

S. Brandt and H.D. Dahmen, The Picture Book of Quantum Mechanics [Science QC174.12.B73 1995].
Generally good for developing that elusive quantal intuition, and particularly good concerning identical particles.

H.J. Lipkin, Quantum Mechanics: New Approaches to Selected Topics [Science QC174.12.L56 1986].
Nice treatment of the second quantization formalism for identical particles.

R.P. Feynman and S. Weinberg, Elementary Particles and the Laws of Physics [Science QC793.28.F49 1987].
The address by Feynman gives a qualitative explanation of the spin-statistics relation.