Graduate Quantum Mechanics

SPRING 2021

Course Number: PHYS 6165

(3 CREDITS, 3 CONTACT HOURS/WEEK)

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

Meeting Times: Monday/Wednesday, 9:30 a.m. - 10:45 a.m.; Location: Online Meetings on Zoom

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

Primary Textbooks:

  • Principles of Quantum Mechanics (Second Edition), R. Shankar

  • Quantum Mechanics: Vols I and II, C. Cohen-Tannoudji, B. Diu & F. Laloe

Secondary Texts:

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

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

Grading Scheme:

  • Homeworks - 60%

  • Mid-term exam - 20%

  • Final Exam (or Presentation) - 20%

  • Extra credit for class participation - up to 5%

Both midterm and final examinations will be open-book take-home exams.

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 proficiency 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:

  • 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 (~ 5 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!). Solutions to the homeworks will not be posted, but can be discussed with/requested from the instructor.

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

  • Absence Policy: Students may not miss a scheduled exam without prior permission from the professor, except in the case of a sudden emergency. If you must miss an exam, please contact the professor as soon as possible to discuss your options.

  • Cell Phones: Use of cell phones is strictly prohibited during lecture hours, except in verifiable cases of emergencies.

  • Food and Drinks: No eatables are allowed during the lecture hours. If you have a compulsive need to eat, please excuse yourself and leave the classroom (or turn off your video/audio in case of zoom) to finish your meal. The exception to this rule is only permitted in case of a medical requirement. The only drink allowed during the lectures is water (feel free to keep yourself hydrated!). Consumption of alcoholic drinks during the lecture is not allowed.

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 ).

Student Mental Health and Well-being: We are a campus that cares about the mental health and well-being of all individuals in our campus community. Your personal health and well-being can impact your success in this course. Students sometimes experience mental health concerns or stressful experiences that interfere with academics and have a negative impact on everyday life. If you or someone you know are experiencing mental health challenges at UMass Lowell, please contact Counseling (information below). Their services are free and confidential, and same day appointments are available.

You can also reach out to any one of a wide range of campus resources, including:

  • Counseling Services provides crisis intervention, assessment, referrals, short-term individual counseling, group therapy, and on-call clinicians outside of business hours. They are located at University Crossing Suite 300 and their 24/7 phone number is 978-934-6800.

  • UMatter2 is a university-wide initiative to support students and promote mental health. The office may be reached at 978-934-6671.

Consider also reaching out to a friend, faculty or family member you trust for help getting connected to the support that can help.

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

  • Continuous and discrete symmetries in quantum mechanics

  • 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: sudden vs adiabatic evolution

  • Second quantization and many-body quantum systems

  • Quantum electrodynamics/Introduction to quantum optics

*Order and topics are subject to change.