Phys 137B: Quantum Mechanics II

Spring 2014

Basic Info

Time: Lectures on Tue and Thu, 5:10-6:30 pm.
Place: 141 Giannini Hall.

Lecturer: Petr Hořava (email: horava@berkeley.edu)
Office: 401 Le Conte.
Office hours: Wednesdays 11am-12noon, Thursdays 2-3pm.
GSI: Kevin Grosvenor (email: kgrosven@berkeley.edu)

Quantum mechanics is absolutely central for our understanding of modern physics: The entire Universe that we live in is quantum mechanical. Moreover, the basic rules, concepts and laws of quantum mechanics appear to be extraordinarily robust and universal, not representing just an approximation to some more fundamental theory, at least to our best knowledge so far. This all makes the learning of the basics of quantum mechanics crucial for everyone who is serious about exact sciences, not stricly speaking only for those with direct research interests in physics.

The basic introduction into the concepts and ideas of quantum mechanics, together with some of the "easy" (and often exactly solvable) examples, is typically covered in the first semester (in a course equivalent to our Phys 137A). In contrast, this second semester of QM will extend the applications of the basic concepts to more complex systems, involving interactions of (often) a large number of constituents. Such more complex systems are certainly more realistic, but also typically not exactly solvable. Extracting useful information about their behavior will require the development of various approximation techniques, of varying level of sophistication. Much of this second semester will be devoted to such perturbative techniques, including the systematic treatment of scattering processes.

The main textbook for this course is going to be:

B.H. Bransden and C.J. Joachain, Quantum Mechanics, 2nd edition (Prentice Hall, 2000),

which I will refer to as [BJ] from now on. This choice of textbook is partially to maintain continuity with the course Phys 137A taught in Fall 2013 by Prof. Siddiqi.

There are now many many more texts on QM, some excellent, some not so much. In the first 80% or so of the semester, we will follow pretty linearly the logic and layout of [BJ], starting from Chapter 8 and ending with Chapter 14. Then, in the final 20% or so of the semester, we will try to have some fun with special, more modern bonus topics -- such as decoherence, quantum entanglement, basics of quantum computing, perhaps even quantum properties of black holes, together with the problems of measurement and interpretation of quantum mechanics, including the Einstein-Podolsky-Rosen paradox and Bell's inequalities, finishing with some possible glimpses into how to expand the framework of QM beyond its existing limits. Hence, the approximate outline of the semester will be as follows:

I. Approximation methods, for time-dependent and time-independent problems;
II. Systems of identical particles and their quantum statistics;
III. Interaction of quantum systems with electromagnetism (both as radiation and as an external field);
IV. Quantum collision theory and scattering processes;
V. Bonus material (to be fine-tuned based on feedback from students in class).

Prerequisites

Introduction to Quantum Mechanics, at the level equivalent to Phys 137A. Roughly, you need to be familiar with the main points of Chapters 1-7 of [BJ] (but, of course, you don't need to know everything that is in those Chapters).

Homeworks and Grading Policy

There will be weekly homework assignments, posted on this website, more info follows below. The final grade will be based on the following breakdown:

50% homeworks (and participation in discussions),
25% midterm exam (given in class in early March),
25% final exam (based primarily on the material of Ch. 8-14 of [BJ]).

Additional info will appear here as it becomes available/relevant.

Homework Assignments

The homework assignments will be posted here weekly, on Thursdays before midnight, and will be due on Thursday, one week later, by 5:10pm, in class (or in place agreed on by the GSI). Most HWs will refer to specific problems in [BJ].

HW1 (due on Thu, Jan 30): Problem 8.2 (on page 427 of [BJ]), Problem 5.13(b) (on page 262), and Problem 8.8 (again on page 427).

HW2 (due on Thu, Feb 6): Problems 8.6, 8.10 and 8.11 (on pages 427-8 of [BJ]).

HW3 (due on Thu, Feb 13): Problems 8.15 and 8.21 (on page 429 of [BJ]).

HW4 (due on Thu, Feb 20): Problems 9.2, 9.6, 9.7 and 9.8 (on pages 466-7 of [BJ]).

HW5 (due on Thu, Feb 27): Problems 10.4, 10.5, 10.6 and 10.7 (on page 512 of [BJ]).

HW6 (due on Thu, March 20): Problems 11.2, 11.5, 11.6, 11.7 and 11.9 (pages 555-6 of [BJ]).

HW7 (due on Thu, April 3): Problems 12.5 and 12.6 (p. 585), and Problem 13.7 (p. 637).

HW8 (due on Thu, April 10): Problems 13.6(a,b) and 13.8(a,b,c) (pp. 636-8). You can also do 13.8(d), but it is not required.

HW9 (due on Thu, April 17): Problems 13.11, 13.12 and 13.14(a) (pp. 638-9).

HW10 (due on Thu, April 24): Problems 14.1, 14.3, 14.4 and 14.5 (p. 676).

Since we are now already in the bonus-material portion of the semester, there will be no new homework assignments. HW10 was the final HW of this course.

horava@berkeley.edu