Instructor: Prof. Seung-Sup Lee (이승섭), Department of Physics and Astronomy, SNU.
TA: Mr. Kiyeon Kim (김기연), Department of Physics and Astronomy, SNU.
Class dates, time, and place: Tuesdays and Thursdays, 11:00–12:15; Rm. 105, Bldg. 56.
Exam times and place: Midterm on Oct. 15 (We), 19:00–22:00; final on Dec. 10 (We), 19:30–22:30; both at Rm. 103, Bldg. 28.
Course outline: Please check the course outline (updated on Dec. 02, 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:
(Required) Jun John Sakurai and Jim Napolitano, Modern Quantum Mechanics (3rd Ed., Cambridge University Press, Cambridge, 2021) (ISBN: 978-1-108-47322-4).
For the first half of the semester, we will cover the topics in this book, often abbreviated to “S&N”. When we refer to sections, equations, figures, problems, etc. without specifying the source, they are assumed to be from S&N.
(Optional, but recommended) Henrik Bruus and Karsten Flensberg, Many-Body Quantum Theory in Condensed Matter Physics: An Introduction (Oxford University Press, Oxford, 2004) (ISBN: 978-0-19-856633-5).
Many lectures during the second half of the semester are based on this textbook. While the lectures will be self-contained, interested students can refer to this comprehensive text for further details. We recommend referring to the corrected version in 2016, which can be identified from the front page (not from the front cover).
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!
[L25.1] Wick's theorem (lecture note) (video)
[L25.2] Interaction picture in the Matsubara formalism (lecture note) (video)
[L25.3] Feynman diagram basics (lecture note) (video)
1. Perturbation series for GF
2. Feynman diagrams for the denominator
3. Feynman diagrams for the numerator
4. Cancellation of disconnected diagrams
5. Self-energy and Dyson equation
No exercises!
[L24.1] Coherent states (lecture note; updated on Nov. 27) (video)
1. Bosonic coherent states
2. Fermionic coherent states
[L24.2] Field integral for the quantum partition function (lecture note; updated on Nov. 27) (video)
No exercises!
[L24.1] Fermi liquid theory (lecture note; updated on Nov. 27) (video)
1. Basic statement
2. Adiabatic continuity
3. Renormalization of the single-particle GF
4. Imaginary part of the self-energy
[L24.2] Bardeen–Cooper–Schrieffer (BCS) theory of superconductivity (lecture note; updated on Nov. 27) (video)
1. BCS Hamiltonian and mean-field approximation
2. BCS mean-field Hamiltonian
3. BCS ground state
4. Self-consistent determination of the BCS order parameter
5. Nambu formalism
No exercises!
Q&A
No exercises!
[L21.1] Interaction picture revisited (lecture note) (video)
[L21.2] Linear response theory (lecture note; updated on Nov. 20) (video)
[L21.3] Kubo formula for the conductivity of continuum systems (lecture note; updated on Nov. 20) (video)
[L21.4] Kubo formula for the dielectric function of continuum systems (lecture note) (video)
[E21] (exercise set; updated on Nov. 20) (solution by 이동규)
Deadline: Nov. 24 (Mo), 23:59
[L20.1] Keldysh formalism (lecture note) (video)
1. Three formalisms for correlation functions in quantum many-body theory
2. Keldysh formalism (KF)
3. Relations between retarded, advanced, and Keldysh GFs
[L20.2] Matsubara formalism (lecture note; updated on Nov. 13) (video)
1. Matsubara GF
2. Fourier transform of Matsubara GF
3. Lehmann representation
4. Matsubara sum
5. Caveat to numerical analytic continuation
[E20] (exercise set) (solution by 강성래)
Deadline: Nov. 19 (We), 23:59
[L19.1] Green’s functions (GFs) (lecture note) (video)
1. GFs in classical electromagnetism
2. GFs in quantum mechanics (not in many-body theory)
3. Single-particle retarded GF of many-body systems
[L19.2] Equation of motion, self-energy (lecture note) (video)
[L19.3] Lehmann representation, spectral function (lecture note) (video)
[E19] (exercise set) (solution by 오세현)
Deadline: Nov. 17 (Mo), 23:59
Q&A
No exercises!
[L17.1] Symmetries (lecture note; updated on Nov. 4) (video)
1. U(1) symmetries
2. SU(2) symmetries
3. Symmetries are useful for solving Hamiltonians
[E17] (exercise set) (solution by 신인섭)
Deadline: Nov. 10 (Mo), 23:59
[L16.1] Some famous models (lecture note) (video)
1. Hubbard atom
2. Hubbard model
3. Anderson impurity model
4. Heisenberg model
5. Kondo model
[L16.2] Schrieffer–Wolff transformation (lecture note; updated on Nov. 7) (video)
[E16] (exercise set) (solution by 강성래)
Deadline: Nov. 05 (We), 23:59
Review and appeal midterm exam grading
[L14.1] Second quantization (lecture note) (video)
1. Bosons
2. Fermions
3. Operators in second quantization
4. Change of basis
5. Field operators
6. Example: non-interacting fermions
[L14.2] Electromagnetic radiation in second quantization (lecture note) (video)
[E14] (exercise set) (solution by 김민재)
Deadline: Oct. 27 (Mo), 23:59
[L13.1] Basics of quantum many-body physics: Intro (lecture note) (video)
[L13.2] Many particles in first quantization (lecture note) (video)
[E13] (exercise set) (solution by 김상헌)
Deadline: Oct. 22 (We), 23:59
Q&A
No exercises!
[L11.1] Partial-wave expansion and phase shifts (lecture note) (video)
[L11.2] Resonance scattering (lecture note) (video)
[E11] (exercise set) (solution by 조현성)
Deadline: Oct. 15 (We), 23:59
[L10.1] Born approximation (lecture note) (video)
1. Born approximation
2. Example: Yukawa potential
[L10.2] Properties of spherical harmonics (lecture note) (video)
1. Spherical harmonics as rotation matrices
2. Addition theorem
3. Spherical wave expansion
[L10.3] Spherical waves (lecture note) (video)
1. Representation in the k-space
2. Representation in the position space
[E10] (exercise set) (solution by 강성래)
Deadline: Oct. 08 (We), 23:59
[L09.1] Scattering amplitude (lecture note)
[L09.2] Optical theorem (lecture note)
It turns out that I recorded another screen, not the correct one that I use for taking notes. So there are no video recordings for Class 09. Sorry for the inconvenience!
[E09] (exercise set) (solution by 박정혁)
Deadline: Oct. 06 (Mo), 23:59
[L08.1] T matrix and S matrix (lecture note; updated on Oct. 14) (video)
1. Derivation using a Green's function
2. Scattering from the future to the past
[E08] (exercise set) (solution by 이연우)
Deadline: Oct. 01 (We), 23:59
Q&A
No exercises!
[L06.1] Geometric phase (lecture note) (video)
1. Berry connection and curvature
2. Correspondence to Aharonov–Bohm effect
3. Example: Spin-1/2 in a B field
[E06] (exercise set) (solution by 김민석)
Deadline: Sep. 24 (We), 23:59
[L05.1] Photoelectric effect (lecture note) (video)
[L05.2] Sudden approximation (lecture note) (video)
[L05.6] Adiabatic approximation (lecture note; updated on Sep. 16) (video)
1. Adiabatic theorem
2. Problem with the traditional adiabatic condition
[E05] (exercise set) (solution by 신인섭)
Deadline: Sep. 22 (Mo), 23:59
[L04.1] Energy shift and decay width (lecture note; updated on Oct. 14) (video)
1. "Slow-turn-on" method
2. Energy shift and decay width
[L04.2] Absorption and emission in a classical radiation field (lecture note; updated on Sep. 11) (video)
1. Absorption and emission rates
2. Electric dipole approximation
[E04] (exercise set) (solution by 남명석)
Deadline: Sep. 17 (We), 23:59
[L03.1] Interaction picture (lecture note; updated on Sep. 9) (video)
1. Recap: Schrödinger vs. Heisenberg picture
2. Interaction picture
3. Example: Rabi oscillations in a spin 1/2
[L03.2] Time-dependent perturbation theory (lecture note; updated on Sep. 16) (video)
1. Transition amplitudes from the Dyson series
2. Constant perturbation: Fermi's golden rule
3. Harmonic perturbation: Stimulated emission and absorption
[E03] (exercise set) (solution by 이규석)
Deadline: Sep. 15 (Mo), 23:59
[L02.1] Zeeman effect (lecture note; updated on Oct. 14) (video)
[L02.2] Variational methods (lecture note) (video)
[E02] (exercise set) (solution by 진승현)
Deadline: Sep. 10 (We), 23:59
[L01.1] Fine structure in hydrogen-like atoms (lecture note; updated on Oct. 14) (video)
1. Relativistic correction to the kinetic energy
2. Spin-orbit coupling
3. Darwin term
[E01] (exercise set) (solution by 조현성)
Deadline: Sep. 08 (Mo), 23:59