Graduate Quantum Mechanics

SPRING 2019

Course Number: PHYS 6150

(3 CREDITS, 3 CONTACT HOURS/WEEK)

Instructor: ARCHANA KAMAL (archana_kamal[AT]uml.edu)

Meeting Times: Tuesday/Thursday, 12:30 - 1:45 p.m.

Location: Kitson 303


Grader: EMERY DOUCET (emery_doucet[AT]student.uml.edu)

Office Hours: By email appointment with the grader (Room # OG-29)


Prerequisites: Undergraduate Quantum Mechanics I and II (or special permission from the instructor).

Primary Textbook: Principles of Quantum Mechanics (Second Edition), R. Shankar.

Secondary Texts:

  • Quantum Mechanics: Fundamentals, K. Gottfried & T. M. Yan

  • Quantum Mechanics (Third Edition), L. D. Landau & E. M. Lifshitz

  • Modern Quantum Mechanics, J. J. Sakurai & J. Napolitano.

Grading Scheme:

  • Homeworks - 50%

  • Mid-term exam - 20%

  • Final exam - 30%

Course Description: This single-semester course assumes prior exposure to quantum mechanics and is designed to train students in more complex concepts and tools of quantum mechanics. By the end of the course, students should have enough exposure in conceptual and technical framework of quantum mechanics to take advanced elective courses, such as quantum Information, quantum optics, quantum field theory, and/or quantum many-body physics.

Course Policy:

  • The students are expected to keep up with the reading of the textbook and/or assigned reading material. Even though this will not directly contribute towards the grade, it is imperative for both digesting the concepts and solving homework problems that employ extensions of concepts introduced in the lecture.

  • Homeworks: All problem sets (~6 in total) will be posted in the shared course folder located on UML one drive (http://onedrive.uml.edu/.). The students will get typically 2 weeks to submit their solutions. No late homeworks will be accepted. To facilitate in-depth learning and maintain fairness, the students should avoid making use of online solutions to problems (if any exist!). Complete solutions to the homeworks will be provided when graded homeworks are returned to the students.

  • Examinations: There will be one mid-term exam and one final exam. The final exam will cover the entire curriculum, but may predominantly focus on the material covered after the mid-term exam.

Academic Integrity: Collaborating with other students on homeworks is encouraged. However, the collective wisdom developed in the process should not preclude individual comprehension. Each student should hand in separate homeworks, written independently of other group members.

Any suspected cheating or other instance of academic dishonesty will be dealt with as per the university policy (please read: https://www.uml.edu/Catalog/Graduate/Policies/AcademicIntegrity.aspx ).

Tentative Course Plan*:

  • Quantum mechanics: framework and basic concepts

  • Path integrals, equivalence to TDSE, instanton tunneling

  • Classical limit: Hamilton's principle, Hamilton-Jacobi equation, Ehrenfest's theorem

  • Charged particle in electromagnetic field: gauge invariance, Landau levels, quantum hall effect.

  • Exactly solvable (low-dimensional) systems: Simple 1D problems, harmonic oscillator, spin/2-level system/qubit

  • NOT-exactly solvable systems: Perturbation theory (Time-independent and time-dependent), Landau-Zener tunneling

  • Second quantization and many-body quantum systems

  • Quantum electrodynamics/Introduction to quantum optics

*Order and topics are subject to change.