PHYC 522/551  Graduate Quantum Mechanics II   Spring 2017

General information          Course overview          Syllabus          Tentative schedule          Problems and Assignments          Exams

General information

Tuesday and Thursday, 9:30-10:45, P&A 184

Lectures (PHYC 522.001):

Friday, 11:00-12:15, P&A 184

Problem (PHYC 551.047):

Professor Akimasa Miyake

office: P&A 25,   email:,   office hours: Tuesday 10:45-12:30, otherwise you may arrange a meeting by appointment.


Bibek Pokharel

office: P&A front area,   email:,   office hours: Thursday 12:30-14:30

Teaching Assistant:

L. E. Ballentine, "Quantum Mechanics: A Modern Development," 2nd Edition, World Scientific (required)


Course overview

This is a graduate core course of quantum mechanics, following PHYC 521 "Graduate Quantum Mechanics I" in Fall 2016. As seen in the syllabus, the basics of quantum mechanics are taught in a self-contained manner at the level more sophisticated than the undergraduate counterpart PHYC 491 and 492. The course is suitable for graduate students or students who have learned quantum mechanics once, in order to brush up understanding of quantum theory and to master its mathematical treatments. We adapt modern pedagogy of active learning in classroom.

Its associated problems session PHYC 551 should be registered as well. It is quite important to do exercise, in order to digest notions and methods in quantum mechanics learned in the lectures. Weekly exercises also facilitate preparations for the preliminary exam. The session is used partially to hold mid-term exams. Roughly speaking, the problems of exams and problem sessions will be selected largely from the exercises at the end of chapters in accordance with the progress of lectures, while those of assignments may be drawn from the past preliminary exams.

The final grade will be determined based on performance of exams and assignments (their weights are 80 % and 20 % respectively, for now). Each mid-term exam is arranged after a couple of chapters are completed. That is how you can study rather narrow, clearly-defined selections of materials for every exam, while they are still fresh in your mind. Overall it is expected that your learning is more effective and at the same time the load by the course is less stressful this way. 


The textbook provides materials enough for a year-long course, so it is expected that we cover roughly a latter half in Spring largely according to the order of chapters. If time permits, I will explain briefly recent research activities related to quantum mechanics and quantum information.

8. State Preparation and Determination   [Lecture note on the chapter 8]

9. Measurement and the Interpretation of States   [Lecture note on the chapter 9]

7. Angular Momentum   [Lecture note on the chapter 7]

12. Time-dependent Phenomena   [Lecture note on the chapter 12]

13. Discrete Symmetries   [Lecture note on the chapter 13]

17. Identical Particles   [Lecture note on the chapter 17]

18. Many Fermion Systems   [Lecture note on the chapter 18]

Tentative schedule

Last updated on February 20, 2017

Jan. 17  Tue
8. State preparation and determination Assignment 1 is posted
Jan. 19  Thu
no lecture

Jan. 20  Fri

no problem session
Jan. 24  Tue
8. State preparation and determination
Jan. 26  Thu
8. State preparation and determination
Jan. 27  Fri

Problem 1
Jan. 31  Tue
8. State preparation and determination
Feb. 2  Thu
8. State preparation and determination
Feb. 3  Fri

Problem 2
Assignment 1 is due
Feb. 7  Tue
8. State preparation and determination
Feb. 9  Thu
8. State preparation and determination
Feb. 10  Fri

Problem 3
Feb. 14  Tue
9. Measurement and the interpretation of states
Feb. 16  Thu
9. Measurement and the interpretation of states
Feb. 17  Fri

Problem 4
Feb. 21  Tue
9. Measurement and the interpretation of states
Assignment 2 is posted
Feb. 23  Thu
no lecture
Feb. 24  Fri

no problem session
Feb. 28  Tue
7. Angular Momentum

Mar. 2  Thu
7. Angular Momentum
Mar. 3  Fri

Problem 5
Mar. 7  Tue
7. Angular Momentum
Mar. 9  Thu
7. Angular Momentum
Mar. 10  Fri

Problem 6
Assignment 2 is due
Mar. 14  Tue
spring break
Mar. 16  Thu
spring break
Mar. 17  Fri
spring break
Mar. 21  Tue

Mar. 23  Thu

Mar. 24  Fri

Mar. 28  Tue

Mar. 30  Thu

Mar. 31  Fri

Apr. 4  Tue

Apr. 6  Thu

Apr. 7  Fri

Apr. 11  Tue

Apr. 13  Thu

Apr. 14  Fri

Apr. 18  Tue

Apr. 20  Thu

Apr. 21  Fri

Apr. 25  Tue

Apr. 27  Thu

Apr. 28  Fri

May 2  Tue

May 4  Thu

May 5  Fri

May 8-12
final week

Problems and Assignments

Students may study subjects of assignments together, but everyone is expected to prepare his/her original answer sheets.

1. Assignment: reviewing the quantum mechanics preliminary exam Spring 2017, due at 12:15 on February 3 (Fri)   [Problems]

2. Assignment, due at 12:00 on March 10 (Fri)   [Problems 8.3, 8.4, 8.5, 8.7, 8.8, 8.10, 9.1, 9.3, 9.4, 9.6     Solutions]

    Note: although some problems have hints in the textbook, you must still answer them by your own words.


Mid-term exams are usually held during the Monday problems session in a closed-book format. No communication with other students is allowed during the exams.

1. Mid-term exam,   [Materials from Chapter X to Chapter Y     Solutions ]