### Course Meeting Times

Lectures: 2 sessions / week, 90 minute / session

Recitations: 2 sessions / week, 1 hour / session

### Prerequisites

Students must have completed *8.03 Physics III: Vibrations and Waves* with a grade of C or higher.

### Description

The course is broadly divided into three parts:

In Part 1, we introduce the basic concepts: Interpretation of the wavefunction, relation to probability, Schrödinger equation, Hermitian operators and inner products. We also discuss wave-packets, time evolution, Ehrenfest theorem and uncertainty.

Part 2 deals with solutions of the Schrödinger equation for one-dimensional potentials. We discuss stationary states and the key problems of a particle moving in: A circle, an infinite well, a finite square well, and a delta-function potential. We examine qualitative properties of the wavefunction. The harmonic oscillator is solved in two ways: Using the differential equation and using creation and annihilation operators. We study barrier penetration and the Ramsaur—Townsend effect.

Part 3 begins with the subject of scattering on the half-line. One can learn in this simpler context the basic concepts needed in 3-dimensional scattering theory: Scattered wave, phaseshifts, time delays, Levinson theorem, and resonances. We then turn to three-dimensional central potential problems. We introduce the angular momentum operators and derive their commutator algebra. The Schrödinger equation is reduced to a radial equation. We discuss the hydrogen atom in detail.

### Required Text

Griffiths, David J. *Introduction to Quantum Mechanics*. Pearson Prentice Hall, 2004. ISBN: 9780131118928.

### References

Shankar, Ramamurti. *Principles of Quantum Mechanics*. Plenum Press, 1994. ISBN: 9780306447907.

(A conceptual textbook with many superb explanations.)

Cohen-Tannoudji, et al. *Quantum Mechanics, Vols. 1 & 2*. Wiley, 1991. ISBN: 9780471164333 and 9780471164357.

(Useful for this course as well as for Quantum Physics II and III. Many students find it too encyclopedic.)

Liboff, Richard L. _Introductory Quantum Mechanic_s. Addison Wesley, 2002. ISBN: 9780805387148.

(A detailed and pedagogic textbook with many exercises.)

Gasiorowicz, Stephen. *Quantum Physics*. Wiley, 2003. ISBN: 9780471057000.

(Efficient textbook, with plenty of material but little explanation.)

Dirac, Paul Adrien Maurice. *The Principles of Quantum Mechanics*. Clarendon Press, 1982. ISBN: 9780198520115.

(Deep, hard and rewarding. Not practical during the semester.)

Ohanian, Hans C. *Principles of Quantum Mechanics*. Prentice Hall, 1989. ISBN: 9780137127955.

### Problem Sets

Weekly problem sets will normally be posted on Thursdays and be due the following Thursday or Friday by 5:00 pm. Solutions will be posted on the due date and graded problem sets will be handed out in recitation sections by the following Thursday.

For practical reasons, late homework will not be graded. For conflicts known in advance (such as religious holidays or travel) problem sets should be turned in before the deadline. Illness or emergencies must be documented if you want to excuse a late homework. To allow for unforeseen circumstances (such as work overload, an annoying headache, forgetting to turn in the p-set on time, etc, etc.) one problem set, either an omitted set or the one with the lowest score, will be removed from the calculation of the homework average.

Sitting down by yourself and reasoning your way through a problem will help you learn the material deeply, identify concepts that are not clear, and develop the analytical skills needed for a successful career in science. If you can solve the problems by yourself, you can expect to do well on the exams. After trying to solve a problem without success, seek help from staff or classmates. Many students learn a great deal from talking to each other. Identify what was preventing you from solving the problem and then solve and write up the solution by yourself.

It is a breach of academic integrity to copy any solution from another student or from previous years’ solutions. Your solutions should be logical, complete, and legible. If you cannot present a solution clearly, it is likely that you do not understand it adequately. Graders are instructed not to give credit for unclear or illegible solutions.

### Exams

Mastery of homework is intended to be the primary learning tool in preparation for exams. There will be two in class tests and one three-hour final exam.

### Grading

The relative weighting of exams and problems sets will be as follows:

Total grade = 75% Exam average + 25% Homework average

Exam average = 0.25 (Test 1 + Test 2) + 0.50 (Final Exam)

The course is not graded on a predetermined curve. If the class as a whole shows unusual mastery of quantum mechanics, the grades will be unusually high. Since we use absolute rather than relative standards, a student cannot lower his or her grade by helping classmates understand the material. Indeed, the process of explaining difficult concepts generally helps clarify and solidify one’s own understanding.