Math 189: Mathematical Methods in Classical and Quantum Mechanics.

Fall 2014


Instructor: David Li-Bland


Office Hours: 1071 Evans Hall, Monday, 9-12am (or by appointment).

Lectures: MWF, 4-5pm, 81 Evans Hall

Course Control Number: 54293

Prerequisites: 104, 110, 2 semesters lower division Physics.

Required Text: Mathematical Methods of Classical Mechanics (Arnol'd)

Description: Geometric methods are playing an increasing role in the study of mechanical systems, both classical and quantum.  In this course, aimed at students majoring in either mathematics, physics, or related fields of science and engineering, I will take a modern approach to mechanics, which emphasizes the role of symmetries and conserved quantities.

On the classical side we will cover both the Lagrangian and Hamiltonian approaches to mechanics. Main topics will include: the principal of least action, Noether’s theorem, Poisson brackets, and holonomic constraints.

On the quantum side we will cover both the Path integral and Schrodinger approaches to quantum mechanics. Main topics will include: the Heisenberg uncertainty relations, Noether’s theorem, and Dirac’s Correspondence principal.

Although the course text is in the series "Graduate Texts in Mathematics", I would like to assure students that Math 189 will be taught at an (advanced) undergraduate level, with an emphasis on concrete examples of the more abstract mathematical structures.


With the exception of exam weeks, there will be weekly homework posted on the course web page, which will be due in class each Wednesday. No late homework will be accepted. 

You are encouraged to discuss ideas with other students. However, you must write and hand in your solutions independently.

A random selection of the assigned homework will be graded. Solutions to the graded exercises will be posted.

When calculating grades, we will drop your two lowest homework scores and use only your remaining scores.

Grading Policy: 

%10 Homework, %20 Midterm I, %20 Midterm II, %45 Final, %5 Participation


  • Midterm Exam 1: Wednesday, September 17th, in class.
  • Midterm Exam 2: Wednesday, October 29th, (take home).
  • Final Exam: Thursday, December 18, 2014 8-11A.

No make-up midterms will be given. If you are absent from one of the midterms, you must have a valid reason and present proof. In such a case, your final exam grade will be substituted for the missed midterm grade.

The L&S student calendar lists drop and grade-change deadlines. The deadline to drop is Friday, September 26th. The first midterm will be marked and returned to you on Wednesday, September 24th.

Participation (5%): You may earn participation points in the following ways:

  • Ask an honest, novel question on Piazza (up to 2%).
  • Provide a helpful, novel answer to another student on Piazza (up to 2%).
  • Earn at least 85% total completion score on the homeworks (up to 1%).


Useful Resources (Recommended Texts, Software, and examples and videos).

Piazza: To handle questions posed outside of class, we will be using Piazza, a free platform for instructors to efficiently manage out-of-class Q&A. On the class dashboard, students can post questions and collaborate Wikipedia-style to edit responses to these questions. Instructors can also answer questions, endorse student answers, and edit or delete any posted content. Instead of emailing me math questions, I encourage you to post them to Piazza.

Each student will be invited to join Piazza by email. Please join it as soon as you can, as I plan to use Piazza extensively. If you do not receive an invitation email, please contact me.

Approach to work and classroom/Piazza interactions:

Please behave according to the academic honor code:

"As a member of the UC Berkeley community, I act with honesty, integrity, and respect for others."

Incomplete grades: Incomplete “I” grades are almost never given. The only justification is a documented serious medical problem or genuine personal/family emergency. Falling behind in this course or problems with workload in other courses are not acceptable reasons.

Special arrangements: If you are a student with a disability registered by the Disabled Student Services (DSS) on UCB campus and if you require special arrangements during exams, you must provide the DSS document and make arrangements via email or office hours at least 10 days prior to each exam, explaining your circumstances and what special arrangements need to be done. Also, see the lecturer as soon as possible to make arrangements for the homeworks.

© David Li-Bland 2014