Instructor: Prof. Seung-Sup Lee (이승섭), Department of Physics and Astronomy, SNU.
TAs: Mr. Jeonghyeok Cha (차정혁) and Mr. Kiyeon Kim (김기연), Department of Physics and Astronomy, SNU.
Class dates, time, and place: Tuesdays and Thursdays, 11:00–12:15; Room 106, Building 56.
Course outline: Please check the course outline (updated on Mar. 08, 2026) for the details. 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: Midterm on April 17 (Fri), 19:00–22:00; final on June 5 (Fri), 19:00–22:00; both at Room 101, Building 28.
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 the Roman alphabet if you don't). Feel free to ask a question in Korean!
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!
Because of Children's Day, there is no on-site class. Please watch the pre-recorded video instead. There are exercises to solve.
[L18.1] Addition of angular momenta (lecture note) (video)
1. Total angular momentum operators; 2. Clebsch–Gordan coefficients and the highest weight construction
[E18] (exercise set)
Deadline: May 11 (Mo), 23:59
[L17.1] Central potentials (lecture note) (video)
1. General properties; 2. Coulomb potential
[E17] (exercise set)
Deadline: May 06 (We), 23:59
Claim for mid-term exam grading
[L15.1] Curvilinear and orthogonal coordinates (lecture note) (video)
1. Curvilinear coordinates in 3D; 2. Jacobians; 3. Orthogonal coordinates; 4. Spherical polar coordinates
[L15.2] Orbital angular momentum and spherical harmonics (lecture note) (video)
1. Orbital angular momentum; 2. Spherical harmonics; 3. Spherical harmonics as rotation matrices
[E15] (exercise set)
Deadline: Apr. 27 (Mo), 23:59
Q&A session only. No exercise!
[L13.1] Eigenvalues and eigenstates of angular momentum (lecture note) (video)
1. Ladder operator method; 2. Block diagonal structure
No exercise!
[L12.1] Angular momentum (lecture note) (video)
1. Angular momentum operators as generators of rotation; 2. Transformation of states and operators according to a rotation; 3. Example: spin-1/2
[L12.2] SU(2) and SO(3) (lecture note) (video)
1. Definition of a group, SU(2), and SO(3); 2. Generators of SU(2) and SO(3); 3. SU(2)–SO(3) homomorphism
[E12] (exercise set) (solution by 권준환)
Deadline: Apr. 15 (We), 23:59
[L11.1] Gauge transformations: scalar potentials (lecture note) (video)
1. Time-dependent potential is trivial if uniform; 2. Example: gravity
[L11.2] Gauge transformations: vector potential (lecture note) (video)
1. Recap: electromagnetism and scalar/vector potentials; 2. Hamiltonian of a charged particle in an EM field; 3. Equation of motion; 4. Schrödinger wave equation and probability current; 5. Aharonov–Bohm effect
[E11] (exercise set) (solution by 권준환)
Deadline: Apr. 13 (Mo), 23:59
[L10.1] Propagators (lecture note) (video)
1. Properties of propagators; 2. Example: a free particle
[L10.2] Feynman's path integrals (lecture note) (video)
1. Feynman's formulation; 2. Equivalence between Feynman's path integral and the Schrödinger wave equation
[E10] (exercise set) (solution by 박아현)
Deadline: Apr. 08 (We), 23:59
[L09.1] Linear potential (lecture note) (video)
1. Solution in terms of the Airy function; 2. Physical example: "bouncing ball"
[L09.2] Wentzel–Kramers–Brillouin (WKB) (semiclassical) approximation (lecture note) (video)
1. Solution away from the classical turning points; 2. Solution near the classical turning points; 3. Matching conditions; 4. "Slowness" criterion; 5. Example: "bouncing ball" revisited
[E09] (exercise set) (solution by 오석훈)
Deadline: Apr. 06 (Mo), 23:59
[L08.1] Schrödinger’s wave equation (lecture note) (video)
1. Time-dependent wave equation; 2. Time-independent wave equation; 3. Example: Free particle with periodic boundary conditions
[L08.2] Simple harmonic oscillator revisited (lecture note) (video)
1. Derivation of the Hermite polynomials and their generating function
[E08] (exercise set) (solution by 최치훈)
Deadline: Apr. 01 (We), 23:59
[L07.1] Simple harmonic oscillator (lecture note) (video)
1. Ladder operator method; 2. Energy eigenstates in the position space; 3. Time evolution
[L07.2] Coherent states (lecture note) (video)
[E07] (exercise set) (solution by 박아현)
Deadline: Mar. 30 (Mo), 23:59
[L06.1] Time evolution: Heisenberg picture (lecture note) (video)
1. Heisenberg equation of motion; 2. Free particles and Ehrenfest theorem
[L06.2] Energy-time uncertainty relation (lecture note) (video)
[E06] (exercise set) (solution by 김대혁)
Deadline: Mar. 25 (We), 23:59
[L05.1] Time evolution: Schrödinger picture (lecture note) (video)
1. Time evolution operator; 2. Schrödinger equation for the time-evolution operator; 3. Time evolution of the density operator
[L05.2] Non-Hermitian Hamiltonians (lecture note) (video)
[E05] (exercise set) (solution by 최치훈)
Deadline: Mar. 23 (Mo), 23:59
[L04.1] Direct sum, tensor product, partial trace (lecture note) (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) (video)
1. Bipartite entanglement, entanglement entropy; 2. CHSH inequality
[E04] (exercise set) (solution by 박아현)
Deadline: Mar. 18 (We), 23:59
[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 operators (lecture note) (video)
1. Density operator; 2. Quantum statistical mechanics
[E03] (exercise set) (solution by 김준원)
Deadline: Mar. 16 (Mo), 23:59
[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) (video)
1. Translation operator; 2. Momentum operator as a generator of translation
[E02] (exercise set) (solution by 김재혁)
Deadline: Mar. 11 (We), 23:59
[L01.1] Dirac's bra-ket notation (lecture note; revised on Mar. 3) (video)
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) (solution by 최인영)
Deadline: Mar. 09 (Mo), 23:59