Graduate Quantum Mechanics I, Spring 2025

Basic info

Instructor: Prof. Seung-Sup Lee (이승섭), Department of Physics and Astronomy, SNU.

TA: Mr. Sanghyun Park (박상현) and Mr. Guedong Park (박규동), Department of Physics and Astronomy, SNU.

Class dates, time, and place: Tuesdays and Thursdays, 14:00–15:15; Room 106, Building 56.

Course outline: Please check the course outline (updated on Mar. 12, 2025) for the details of the course. Please check the course outline regularly, since it will be updated from time to time; we will also announce critical changes via eTL.

Textbook: Jun John Sakurai and Jim Napolitano, Modern Quantum Mechanics (3rd Ed., Cambridge University Press, Cambridge, 2020) (ISBN: 978-1-108-47322-4). When we refer to sections, equations, figures, problems, etc. without specifying the reference, they are assumed to be from this book, often abbreviated to S&N.

Exam times and place: Mid-term on April 16 (Wed), 19:00–22:00; final on June 11 (Wed), 19:00–22:00; Room 105, Building 56. (The same floor as the lecture place, but on the opposite side!)

Student Q&A forum: In this KakaoTalk chat (link), students can ask questions, answer them, and discuss any topic. You can join anonymously, but we recommend using your real name (a Korean name if you have one, or in Roman alphabets if you don't). Feel free to ask a question in Korean!

Lecture materials

The list below provides the links to lecture notes, exercises, and their solutions. The lecture notes are numbered as Lxx.y (e.g., L02.1), where xx indexes a class within the semester and y indexes a topic within the class. The exercise sets are similarly numbered as Exx, and an exercise within a set as Exx.y.

Please refer to the course outline (see above) for the details: when lecture materials will be uploaded, how to prepare and submit exercise solutions, etc.

Please report if you find any mistakes or typos. Such reports will also count towards the evaluation!

[Class 04] Mar. 13 (Th)

• [L04.1] Direct sum, tensor product, partial trace (lecture note; typo fixed on Mar. 13) (video)
  1. Direct sum; 2. Tensor product; 3. Partial trace

• [L04.2] Singular value decomposition and Schmidt decomposition (lecture note) (video)

• [L04.3] Entanglement and Bell inequalities (lecture note; minor update on Mar. 13) (video)
  1. Bipartite entanglement, entanglement entropy; 2. CHSH inequality

• [E04] (exercise set)
  Deadline: Mar. 19 (We), 23:59

[Class 03] Mar. 11 (Tu)

• [L03.1] Baker–Hausdorff lemma and Baker–Campbell–Hausdorff formula (lecture note) (video)
  1. BH lemma with its proof; 2. BCH formula with its proof

• [L03.2] Density operator (lecture note; updated on Mar. 12) (video)
  1. Density operator; 2. Quantum statistical mechanics

• [E03] (exercise set; note added on Mar. 13)
  Deadline: Mar. 17 (Mo), 23:59

[Class 02] Mar. 07 (Th)

• [L02.1] Unitary transformation (lecture note) (video)
  1. Change of basis; 2. Diagonalization; 3. Analytic functions of operators; 4. Unitary as the exponential of a Hermitian; 5. Trace

• [L02.2] Position and momentum (lecture note; typo fixed on Mar. 6) (video 1/2) (Sorry, I forgot to record 2/2...)
  1. Translation operator; 2. Momentum operator as a generator of translation

• [E02] (exercise set)
  Deadline: Mar. 12 (We), 23:59

[Class 01] Mar. 04 (Tu)

• [L01.1] Dirac's bra-ket notation (lecture note) (video 1/2) (video 2/2)
  1. Kets, bras, and operators in the Hilbert space; 2. Matrix representations; 3. Example: spin-1/2

• [L01.2] Measurements and uncertainty relations (lecture note) (video)
  1. Measurements, compatible (commuting) observables; 2. Uncertainty relations: Robertson–Schrödinger relation and its proof

• [E01] (exercise set)
  Deadline: Mar. 10 (Mo), 23:59

[Previous exam problems]

• Mid-term exam for the Spring 2023 semester (problems)