Graduate Quantum Mechanics

SPRING 2020

Course Number: PHYS 6165

(3 CREDITS, 3 CONTACT HOURS/WEEK)

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

Meeting Times: Tuesday/Thursday, 8:00 a.m. - 9:15 a.m.; Location: Olsen 353

Meeting Times*: Monday, 8:30 a.m. - 10:30 a.m.; Location: Online Meetings on Zoom


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

Office Hours: Walk-in/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 (Third Edition), L. D. Landau & E. M. Lifshitz

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

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

Grading Scheme*:

  • Homeworks - 50% 80%

  • Mid-term exam - 20%

  • Final exam - 30%

  • Extra credit for class participation - up to 5%

*In view of movement to online instruction, starting 03/18/2020, due to covid-19.

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 eld 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 4 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 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 and Other Devices: Use of cell phones is strictly prohibited during lecture hours, except in verifiable cases of emergencies. Use of laptops and electronic tablets is limited to the instances when required for in-class exercises or running simulations explicitly provided during the course of the lectures. Students who prefer to take notes on electronic writing pads or tablets, should contact the professor and seek prior permission to do so.

  • 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 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!). No soft or alcoholic drinks are allowed in the class.

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

  • 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.