Quantum Mechanics

Oberlin College Physics 312

Syllabus for Fall 20XX

Instructor: Dan Styer, Wright Laboratory 215, 775-8183, Dan.Styer@oberlin.edu
home telephone 775-0959 (6 pm to 9 pm only, please).

Meeting times: Class: MWF at 9:00 am. Conference: Monday at 3:30 pm.

Prerequisites: Before taking this course, you are required to have taken Physics 112, Modern Physics, Physics 310, Classical Mechanics, and Mathematics 234, Differential Equations. It is also helpful, although not required, for you to have taken Mathematics 232, Linear Algebra.



  1. Conceptual foundations.
    Why do we need a quantum mechanics? The Stern-Gerlach experiment and two-state systems. Probability, interference, entanglement. What is a quantal state?
  2. Forging mathematical tools for quantum mechanics.
    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 and for the time development problem.
  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. Conceptual foundations.
    Quantal motion as a sum over classical paths.

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 given the fifth and tenth weeks of the semester. Exams will cover topics from lectures and problem sets rather than from readings.

Problem sets will be distributed on each Wednesday, except for the Wednesdays preceding the exams. Each is due in class the following Wednesday; late papers will be accepted only in cases of illness. When writing your solutions, be sure to describe (in words) the thought that went into your work as well as describing (in equations) the mathematical manipulations involved. The lowest two of your homework scores will be discarded and the remainder 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.

Quantum Mechanics Bibliography

You are of course free to disregard the assigned texts and use whatever materials you desire. Here are some books on reserve in the science library.

Popular works:

D.F. Styer, The Strange World of Quantum Mechanics.
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.
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:

R. Shanker, Principles of Quantum Mechanics.
Nice discussions, conversational tone.

R.L. Liboff, Introductory Quantum Mechanics.
Has been used as the text for this course in the past.

R.G. Winter, Quantum Physics, second edition.
Another text previously used in this course.

R.W. Robinett, Quantum Mechanics: Classical Results, Modern Systems, and Visualized Examples.
A wonderful book, but not well-matched to this course. The author's errata list is at http://www.phys.psu.edu/ROBINETT/BOOK/book_refs.html.

J.S. Townsend, A Modern Approach to Quantum Mechanics.
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.

D. Park, Introduction to the Quantum Theory.
The old standard of undergraduate quantum mechanics texts.

Graduate level texts:

E. Merzbacher, Quantum Mechanics.

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

J.J. Sakurai, Modern Quantum Mechanics.

A. Messiah, Quantum Mechanics.

K. Gottfried, Quantum Mechanics.
Unconventional. Don't look for volume two...it doesn't exist.

G. Baym, Lectures on Quantum Mechanics.

L.I. Schiff, Quantum Mechanics.
The grand old man of graduate quantum mechanics texts. Based on Oppenheimer's lectures.

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

P.A.M. Dirac, The Principles of Quantum Mechanics, fourth edition.
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.

T.F. Jordan, Quantum Mechanics in Simple Matrix Form.

R.P. Feynman, R.B. Leighton and M. Sands, The Feynman Lectures on Physics, volume 3.

R.P. Feynman and A.R. Hibbs, Quantum Mechanics and Path Integrals, chapter 1.

G. Greenstein and A. Zajonc, The Quantum Challenge: Modern Research on the Foundations of Quantum Mechanics.
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.
An exceptionally clear treatment of the formalism of quantum mechanics.

J.R. Hiller, I.D. Johnston, and D.F. Styer, Quantum Mechanics Simulations.
Software and book.

R.N. Zare, Angular Momentum: Understanding Spatial Aspects in Chemistry and Physics.

S. Brandt and H.D. Dahmen, The Picture Book of Quantum Mechanics.
Generally good for developing that elusive quantal intuition, and particularly good concerning identical particles.

H.J. Lipkin, Quantum Mechanics: New Approaches to Selected Topics.
Nice treatment of the second quantization formalism for identical particles.

R.P. Feynman and S. Weinberg, Elementary Particles and the Laws of Physics.
The address by Feynman gives a qualitative explanation of the spin-statistics relation.