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 Apr. 21, 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, at Room 105, Building 56; final on June 11 (Wed), 19:00–22:00, at Room 102, 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 Roman alphabets 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!
Exam problems and solutions (to be posted)
[L25.1] Time-independent perturbation theory: degenerate case (lecture note) (video)
1. First order; 2. Second order
[E25] (exercise set)
Deadline: Jun. 04 (We), 23:59
[L24.1] Time-independent perturbation theory: non-degenerate case (lecture note) (video)
1. Energy shifts and changes of eigenstates; 2. Wave function renormalization
[E24] (exercise set)
Deadline: Jun. 02 (Mo), 23:59
[L23.1] Time-reversal symmetry (lecture note)
1. Anti-unitary operators; 2. Time reversal operator; 3. Important theorems, including Kramers degeneracy
[E23] (exercise set)
Deadline: May 28 (We), 23:59
[L22.1] Lattice translation symmetry and Bloch’s theorem (lecture note) (video)
1. Lattice translation operator and its eigenstates; 2. Bloch's theorem; 3. Ex. Tight-binding model
[E22] (exercise set)
Deadline: May 26 (Mo), 23:59
[L21.1] Parity symmetry (lecture note) (video)
1. Recap: Symmetries in QM; 2. Parity operator
[E21] (exercise set)
Deadline: May 21 (We), 23:59
[L20.1] Tensor operators (lecture note) (video)
1. Motivation; 2. Vector operators; 3. Irreducible representations of tensor operators under rotations
[L20.2] Product of tensor operators (lecture note) (video)
[L20.3] Wigner–Eckart theorem (lecture note) (video)
[E20] (exercise set)
Deadline: May 19 (Mo), 23:59
[L19.1] Schwinger's oscillator model of angular momentum (lecture note) (video)
1. Oscillator model; 2. Explicit formula for rotation matrices
[E19] (exercise set)
Deadline: May 14 (We), 23:59
Because of the substitute holiday for Buddha's birthday, 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; typo fixed on May 8) (video)
1. Total angular momentum operators; 2. Clebsch–Gordan coefficients and the highest weight construction
[E18] (exercise set) (solution by 오민석)
Deadline: May 12 (Mo), 23:59
[L17.1] Central potentials (lecture note) (video)
1. General properties; 2. Coulomb potential
[E17] (exercise set) (solution by 안정하)
Deadline: May 07 (We), 23:59
Claim for mid-term exam grade
[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
[E15] (exercise set) (solution by 안정하)
Deadline: Apr. 28 (Mo), 23:59
[L14.1] Eigenvalues and eigenstates of angular momentum (lecture note) (video)
1. Ladder operator method; 2. Block diagonal structure
[E14] (exercise set) (solution by 이승민)
Deadline: Apr. 23 (We), 23:59
Q&A session only. No exercises!
[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 조현성)
Deadline: Apr. 17 (Th), 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 신인섭)
Deadline: Apr. 14 (Mo), 23:59
[L10.1] Propagators (lecture note; minor update on Apr. 03) (video)
1. Properties of propagators; 2. Example: a free particle
[L10.2] Feynman's path integrals (lecture note; minor update on Apr. 03) (video)
1. Feynman's formulation; 2. Equivalence between Feynman's path integral and the Schrödinger wave equation
[E10] (exercise set; minor update on Apr. 09) (solution by 이동규)
Deadline: Apr. 09 (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; minor update on Apr. 01) (solution by 신인섭)
Deadline: Apr. 07 (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 안정하)
Deadline: Apr. 02 (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; typo fixed on Mar. 25) (video)
[E07] (exercise set) (solution by 신인섭)
Deadline: Mar. 31 (We), 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 김선규)
Deadline: Mar. 26 (We), 23:59
[L05.1] Time evolution: Schrödinger picture (lecture note) (video; the middle part of the lecture is not recorded by mistake)
1. Time evolution operator; 2. Schrödinger equation for the time-evolution operator; 3. Time evolution of density operator
[L05.2] Non-Hermitian Hamiltonians (lecture note) (video)
[E05] (exercise set; note added on Mar. 18) (solution by 최치훈)
Deadline: Mar. 24 (Mo), 23:59
[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) (solution by 김민석)
Deadline: Mar. 19 (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 operator (lecture note; updated on Mar. 12) (video)
1. Density operator; 2. Quantum statistical mechanics
[E03] (exercise set; note added on Mar. 13) (solution by 김민우)
Deadline: Mar. 17 (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; minor revision on Mar. 20) (video 1/2) (Sorry, I forgot to record 2/2...)
1. Translation operator; 2. Momentum operator as a generator of translation
[E02] (exercise set) (solution by 진승현)
Deadline: Mar. 12 (We), 23:59
[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) (solution by 이수창)
Deadline: Mar. 10 (Mo), 23:59