Fall-2020. Math 189 (ccn 32196): Mathematical Methods in Classical and Quantum Mechanics

Instructor: Alexander Givental
Lectures: TuTh 9:30-11 on Zoom
Enroled students should have received an email from me with the link to join the Zoom lectures. If you haven't received the link, or not enrolled, but want to audit the course, send me an email request from your UC Berkeley email account.
Prerequisites: Strong command of Math 53 and Math 54, upper-division level of mathematical maturity; Math 110, Math 113 and 2 semesters of physics are recommended.
Description: In this reincarnation of the course, we will follow closely the instructor's own
"Introduction to Quantum Mechanics"
As can be seen from the book's Preface, it will be an attempt to understand physics, yet from a point of view that might be appealing to a mathematician. The emphasis will be on quantum mechanics, although some brief (an certainly insuficient) excursions into Hamiltonian and Lagrangian classical mechanics will also occur. Formal mathematical rigor will be a second priority. Respectively, Math 53 and Math 54 will suffice as the starting prerequisites. The students will be expected, however, to digest quickly many new (and often abstract) ideas. So, by the required degree of general mathematical maturity, this course will perhaps be on a par with other senior level electives.
Office Hours: weekly Tue, 7-9 pm Berkeley time (on the same zoom as lectures)
Grading: 1/5 final + 4/5 homework; I have, however, the following (ingenious, in my view) grading scheme. The score of any particular homework problem which is below your score on the final will be dropped - together with its weight in the total grade. E.g. if half of your hw is below the final score, then only the other half counts, but it weighs 2/3 rather than 4/5, while the final score weighs 1/3 rather than 1/5.
Homework: weekly, posted to this website; due Th "in class", i.e. before the start of lecture by email (givental-at-math-dot-berkeley-dot-edu) in pdf format
Final: most likely "take home"

Here is the list of exercises to the textbook. It will grow during the semester, and the exercises whose solutions are to be submitted by you as written homework will be assigned from this list. Solving all other exercises from the list is highly recommended, and is probably necessary for understanding the material.

Homework scores:
"+" = "problem is solved"
"+/-" = "problem is essentially solved, but there are some gaps which the author should be able to fill in"
"+/2" = "about half of the wprk done"
"-/+" = "problem is unsolved, but there is substantial progress which can lead to a complete solution"
"-" = "problem is unsolved"
As a tentative translation into a letter grade, think of these signs as roughly "+" = "in the A range", "+/-" = "in the B range", "+/2" = "in the C range", "-/+" = "in the D range".

HW1, due Th, Sep. 3: Read pp. 1-16 (1-8 for Lecture 1). Solve exercises 1.4 and 2.4 from the list (i.e. exercise 4 to section 1 and ecercise 4 to Section 2).
HW2, due Th, Sep. 10: Read p.27 (Time-dependent hamiltonians), Section 3(in this order). Solve exercises 2.6, and 3.4.
HW3, due Th, Sep. 17: Read Section 4 and pages 31-34 from Section 5. Solve exercises 3.5 and 4.3.
HW4, due Th, Sep. 24: Read Section 5 to the end. Solve exercises 5.7 and 5.10.
HW5, due Th, Oct. 1: Read Section 6. Solve exercises 5.12 and 5.14.
HW6, due Th, Oct. 8: Read Section 7. Solve exercises 6.8 and 6.13.
HW7, due Th, Oct. 15: Sections 8 and 9 (about the hydrogen model and spin) form the central theme of the subject we are studying. Read very closely (and prior to the lectures!) pages 65-70 from Section 8. Solve exercises 7.5 and 7.6.
HW8, due Th, Oct. 22: Read Section 8 to the end, and Section 9 up to page 82. Solve exercises 8.6 and 8.10.
HW9, due Th, Oct. 29: Read Section 9 to the end. Solve exercises 8.14 and 9.9.
HW10, due Th, Nov. 5: Read Section 10. Solve exercises 9.19 and 9.20.
HW11, due Th, Nov. 12: Read Section 11. Solve exercises 10.3 and 10.9.
HW12, due Th, Nov. 19: Read Section 12 minus the last subsection on Korteweg -- de Vries. Solve 11.1 and 11.8.
HW13, due Th, Dec. 3: Read subsection on Korteweg -- de Vries by Tue, Nov. 24 , read Section 13 during (or instead of) the Thanksgiving break. Solve three exercises: 12.8, 12.11, 12.16, and submit their solutions by Th, Dec. 3 (the week after Thanksgiving).
HW14, due Th, Dec. 10: Read Section 14. Solve exercises 13.3 and 13.8.

Answers to hw problems

Also: I have suggested (correctly) that you download the text in order to enable hyper-references. However, I keep finding typos in the text and occasionally update the file online. So, you might want to occasionally update your copy too.

Lecture notes