PHYC 521/551  Graduate Quantum Mechanics I   Fall 2016


General information          Course overview          Syllabus          Tentative schedule          Problems and Assignments          Exams


General information


Monday and Wednesday, 11:00-12:15, P&A 5

Lectures (PHYC 521.001):

Monday, 17:30-18:45, P&A 184

Problem (PHYC 551.057):

Professor Akimasa Miyake

office: P&A 25,   email: amiyake_at_unm.edu,   office hours: Monday 14:00-16:00, otherwise you may arrange a meeting by appointment.

Instructor:

Bibek Pokharel

office: P&A front area,   email: bibekpokharel_at_unm.edu,   office hours: Thursday 8:45-10:45 

Teaching Assistant:

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

Textbook:



Course overview


This is a graduate core course of quantum mechanics, and continues to PHYC 522 "Graduate Quantum Mechanics II" in Spring 2017. 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. 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. 



Syllabus

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

0. Introduction   [Lecture note on the chapter 0]

1. Mathematical Prerequisites   [Lecture note on the chapter 1]

2. The Formulation of Quantum Mechanics   [Lecture note on the chapter 2]

3. Kinematics and Dynamics   [Lecture note on the chapter 3]

4. Coordinate Representation and Applications   [Lecture note on the chapter 4]

5. Momentum Representation and Applications   [Lecture note on the chapter 5]

6. The Harmonic Oscillator   [Lecture note on the chapter 6]



Tentative schedule

Last updated on December 21, 2016

Dates
Subjects
Assignments/Exams
Aug. 22  Mon
 0. Introduction no Problem session
Aug. 24  Wed
1. Mathematical Prerequisites
Assignment 1 is posted
Aug. 29  Mon
1. Mathematical Prerequisites Problem 1 (Prob 1.1)
Aug. 31  Wed
1. Mathematical Prerequisites
Sep. 5  Mon
Labor day holiday
Sep. 7  Wed
2. Foundation of Quantum Mechanics

Sep. 12  Mon
2. Foundation of Quantum Mechanics Problem 2 (Prob 1.2, 1.3, 2.2)
Assignment 1 is due
Sep. 14  Wed
2. Foundation of Quantum Mechanics
Sep. 19  Mon
2. Foundation of Quantum Mechanics Problem 3 (Prob 1.4, 1.5, 2.5)
Sep. 21  Wed
3. Kinematics and Dynamics

Sep. 26  Mon
3. Kinematics and Dynamics Mid-term exam 1
Assignment 2 is due
Sep. 28  Wed
3. Kinematics and Dynamics
Oct. 3  Mon
3. Kinematics and Dynamics Problem 4 (commutation relation (c),
Prob 2.8)
Oct. 5  Wed
3. Kinematics and Dynamics
Oct. 10  Mon
3. Kinematics and Dynamics Problem 5 (commutation relation (f),
exponential maps)
Oct. 12  Wed
3. Kinematics and Dynamics
Oct. 17  Mon
3. Kinematics and Dynamics Problem 6 (Prob 3.3,
commutation relation [J, Q])
Oct. 19  Wed
3. Kinematics and Dynamics
Oct. 24  Mon
4. Coordinate representation and applications
Problem 7 (Prob 3.8, 3.4)
Oct. 26  Wed
4. Coordinate representation and applications
Oct. 31  Mon
4. Coordinate representation and applications Problem 8 (commutation relation [Q^n, P],
Ehrenfest relation)
Assignment 3 is due 
Nov. 2  Wed
4. Coordinate representation and applications
Nov. 7  Mon
4. Coordinate representation and applications Problem 9 (tunneling problem in page 112)
Nov. 9  Wed
5. Momentum representation and applications
Nov. 14  Mon
5. Momentum representation and applications
Mid-term exam 2
Nov. 16  Wed
5. Momentum representation and applications
Nov. 21  Mon
5. Momentum representation and applications Problem 10 (time evolution of
a free particle in page 145) 
Nov. 23  Wed
6. Harmonic oscillator

Nov. 28  Mon
6. Harmonic oscillator Problem 11 (Prob 5.5, 6.1)
Nov. 30  Wed
6. Harmonic oscillator
Dec. 5  Mon
6. Harmonic oscillator Problem 12 (Prob 6.1)
Dec. 7  Wed
6. Harmonic oscillator
Dec. 12-15
final week
Assignment 4 is due
Final exam 3
 



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 Fall 2016, due at 17:30 on September 12 (Mon)   [Problems]

2. Assignment, due at 17:00 on September 26 (Mon)   [Problems in page 39-40 1.9, 1.12, 1.14, 1.15, 1.16    Solutions]

3. Assignment, due at 17:30 on October 31 (Mon)   [Problems 2.9, 3.1, 3.2, 3.6, 3.11    Solutions]

4. Assignment, due at 17:00 on December 12 (Mon)   [Problems 4.9, 4.11, 5.3, 5.8, 6.5, 6.7, 6.8    Solutions]




Exams


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, 17:00-19:00 on September 26 (Mon)   [Materials from Chapter 0 to Chapter 2     Solutions ]

2. Mid-term exam, 17:00-19:00 on November 14 (Mon)   [Materials from Chapter 3 to Chapter 4 Section 4.7     Solutions ]

3. Final exam, 10:00-12:00 on December 14 (Wed) at P&A 184   [Materials from Chapter 4 Section 4.8 to Chapter 6     Solutions ]