Math 189 -- Mathematical Methods in Classical and Quantum Mechanics


Instructor: Yael Karshon , karshon@math.berkeley.edu
Lectures: Tue Thu 9:30 -- 11:00, 55 Evans Hall
Office: 867 Evans Hall, (510) 643-7543
Office hours: Mondays 9:30 - 12:30

Grading: Grading will be based on class participation, weekly homework, one midterm, an essay or (possibly a take-home) final.

Required text: V. I. Arnold, Mathematical Methods of Classical Mechanics, Second Edition, Springer-Verlag, 1989.

Recommended texts:
P. Bamberg and S. Sternberg, A course in mathematics for students of physics 2, Cambridge University Press, 1990.
R. L. Faber, Differential geometry and relativity theory .
G. Fano, Mathematical Methods of Quantum Mechanics, McGraw-Hill, 1971.

Comments: This course will emphasize the geometry underlying physical models.
In the first part of the course we will follow Arnold's book on the following topics: Motion in phase space, symmetries and momentum, calculus of variations, Lagrangian mechanics on manifolds, differential forms, symplectic mechanics.
In the second part of the course we will discuss additional topics, such as special relativity, electromagnetism, thermodynamics, quantum mechanics. We will use the recommended texts listed above. Relevant written material (notes and/or some relevant pieces of the texts) will be made available to the students.

Problem sets

You are encouraged to work on the problem sets together with each other. However, you are required to write up the answers by yourself. If you don't complete the problem set in time, you are welcome to submit partial answers. Clarity is crucial. Be clear on what you did and what you did not do; if you did not solve a problem, don't hide it with many words.

Problem set 1: ps , pdf . Solutions were handed out in class.

Problem set 2: ps , pdf . Solutions: ps , pdf .

Problem set 3: ps , pdf . Solutions: ps , pdf .

Problem set 4 was handed out in class, and so were its solutions.

Problem set 5: ps , pdf . Solutions were handed out in class.

Problem set 6: ps , pdf .

Problem set 7: ps , pdf .

Problem set 8: ps , pdf .