Instructor: Prof. Seung-Sup Lee (이승섭), Department of Physics and Astronomy, SNU.
TA: Mr. Sanghyun Park (박상현), Department of Physics and Astronomy, SNU.
Class dates, time, and place: Tuesdays and Thursdays, 14:00–15:15; Rm. 105, Bldg. 56.
Course outline: Please check the course outline (updated on Nov. 13, 2024) for the details of the course. Please check the course outline regularly, since it will be updated from time to time; critical changes will be also announced via eTL.
Textbooks:
(Required) Jun John Sakurai and Jim Napolitano, Modern Quantum Mechanics (3rd Ed., Cambridge University Press, Cambridge, 2020) (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 comprehensive textbook. While the lectures will be self-contained, interested students can refer to this 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 Q&A in Korean!
Exam times and place: Mid-term on Oct. 29 (Tu), 19:00–22:00; final on Dec. 12 (Th), 19:00–22:00; Rm. 105, Bldg. 56.
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!
Mid-term exam for the fall 2023 semester (problems)
Final exam for the fall 2023 semester (problems) (solutions)
Q&A
No exercises!
[L25.1] Coherent states (lecture note)
1. Bosonic coherent states
2. Fermionic coherent states
[L25.2] Field integral for the quantum partition function (lecture note)
[L24.1] Fermi liquid theory (lecture note) (video)
1. Basic statement
2. Adiabatic continuity
3. Renormalization of the single-particle GF
[L24.2] Bardeen–Cooper–Schrieffer (BCS) theory of superconductivity (lecture note; small note added on Dec. 05) (video)
1. BCS Hamiltonian and mean-field approximation
2. BCS ground state
3. Self-consistent determination of the BCS order parameter
4. Nambu formalism
No exercises!
Q&A
No exercises!
This class was hybrid (on-site + Zoom). The video recording for the whole class: (part 1) (part 2)
[L22.1] Interaction picture revisited (lecture note)
[L22.2] Linear response theory (lecture note)
[L22.3] Kubo formula for the conductivity (lecture note; typo fixed on Nov. 28)
[L22.4] Kubo formula for the dielectric function (lecture note)
[E22] (exercise set) (solution by 박창현)
Deadline: Dec. 04 (We), 23:59
Since the instructor is traveling, there is no on-site class. Please watch the video recording of the lecture instead. There are exercises to solve.
[L21.1] Keldysh formalism (lecture note) (video)
1. Three formalisms for correlation functions in quantum many-body theory
2. Keldysh formalism (KF)
3. Relations among retarded, advanced, and Keldysh GFs
[L21.2] Matsubara formalism (lecture note) (video)
1. Matsubara GF
2. Fourier transform of Matsubara GF
3. Lehmann representation
4. Matsubara sum
5. Caveat to numerical analytic continuation
[E21] (exercise set) (solution by 박창현)
Deadline: Dec. 02 (Mo), 23:59
Due to university admissions, there is no on-site class. Please watch the video recording of the lecture instead. There are exercises to solve.
[L20.1] 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
[L20.2] Equation of motion, self-energy (lecture note) (video)
[L20.3] Lehmann representation, spectral function (lecture note; mistakes fixed on Dec. 12) (video)
[E20] (exercise set) (solution by 정현성)
Deadline: Nov. 27 (We), 23:59
Q&A
No exercises!
[L18.1] Symmetries (lecture note) (video)
1. U(1) symmetries
2. SU(2) symmetries
3. Symmetries are useful for solving Hamiltonians
[E18] (exercise set) (solution by 박창현)
Deadline: Nov. 20 (We), 23:59
[L17.1] Some famous models (lecture note) (video)
1. Hubbard atom
2. Hubbard model
3. Anderson impurity model
4. Heisenberg model
5. Kondo model
[L17.2] Schrieffer–Wolff transformation (lecture note; typo fixed on Nov. 12) (video)
[E17] (exercise set; a note added on Nov. 15) (solution by 박창현 & 정현성)
Deadline: Nov. 18 (Mo), 23:59
Review and appeal mid-term exam grading; no exercises!
Since the instructor is traveling, there is no on-site class. Please watch the video recording of the lecture instead. There are exercises to solve.
[L15.1] Second quantization (lecture note) (video)
1. Bosons
2. Fermions
3. Operators in the second quantization
4. Change of basis
5. Field operators
6. Example: non-interacting fermions
[L15.2] Electromagnetic radiation in the second quantization (lecture note) (video)
[E15] (exercise set) (solution by 정현성)
Deadline: Nov. 11 (Mo), 23:59
[L14.1] Basics of quantum many-body physics: Intro (lecture note; updated on Oct. 31)
[L14.2] Many particles in the first quantization (lecture note; updated on Oct. 31)
[E14] (exercise set) (solution by 오세욱)
Deadline: Nov. 06 (We), 23:59
Q&A
No exercises!
[L12.1] Hard-sphere scattering (lecture note)
[L12.2] Low-energy scattering (lecture note)
[L12.3] Resonance scattering (lecture note)
[E12] (exercise set) (solution by 이성빈)
Deadline: Oct. 23 (We), 23:59
[L11.1] Partial-wave expansion and phase shifts (lecture note)
[L11.2] Determination of phase shifts (lecture note)
[E11] (exercise set) (solution by 김현우)
Deadline: Oct. 21 (Mo), 23:59
[L10.1] Born approximation (lecture note)
1. Born approximation
2. Example: Yukawa potential
[L10.2] Properties of spherical harmonics (lecture note)
1. Spherical harmonics as rotation matrices
2. Addition theorem
3. Spherical wave expansion
[L10.3] Spherical waves (lecture note)
1. Representation in the k-space
2. Representation in the position space
[E10] (exercise set; typo fixed on Oct. 15) (solution by 오세욱)
Deadline: Oct. 16 (We), 23:59
[L08.1] Scattering amplitude (lecture note)
[L08.2] Optical theorem (lecture note)
[E08] (exercise set) (solution by 박창현)
Deadline: Oct. 14 (Mo), 23:59
Since Oct. 01 is a temporary holiday, there is no on-site class. Please watch the video recording of the lecture instead. There are exercises to solve.
[L08.1] T matrix and S matrix (lecture note) (video)
1. Derivation by using Green's function
2. Scattering from the future to the past
[E08] (exercise set) (solution by 오세욱)
Deadline: Oct. 07 (Mo), 23:59
Q&A
No exercises!
[L06.1] Geometric phase (lecture note)
1. Berry connection and curvature
2. Correspondence to Aharonov–Bohm phase
3. Example: Spin-1/2 in a B field
[E06] (exercise set) (solution by 정현성)
Deadline: Sep. 30 (Mo), 23:59
[L05.1] Photoelectric effect (lecture note)
[L05.2] Sudden approximation (lecture note)
[L05.6] Adiabatic approximation (lecture note)
1. Adiabatic theorem
2. Problem with traditional adiabatic condition
[E05] (exercise set) (solution by 박창현)
Deadline: Sep. 25 (We), 23:59
[L04.1] Energy shift and decay width (lecture note)
1. "Slow-turn-on" method
2. Energy shift and decay width
[L04.2] Absorption and emission in a classical radiation field (lecture note)
1. Absorption and emission rates
2. Electric dipole approximation
[E04] (exercise set; mistake fixed on Sep. 15; updated on Sep. 20) (solution by 정현성)
Deadline: Sep. 21 (Sa), 23:59
[L03.1] Interaction picture (lecture note)
1. Recap: Schrödinger vs. Heisenberg picture
2. Interaction picture
3. Example: Rabi oscillations in a two-level system
[L03.2] Time-dependent perturbation theory (lecture note)
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 박창현)
Deadline: Sep. 16 (Mo), 23:59
[L02.1] Zeeman effect (lecture note)
[L02.2] Variational methods (lecture note)
[E02] (exercise set) (solution by 정현성)
Deadline: Sep. 11 (We), 23:59
[L01.1] Fine structure in hydrogen-like atoms (lecture note)
1. Relativistic correction to the kinetic energy
2. Spin-orbit coupling
3. Darwin term
[E01] (exercise set) (solution by 이성민)
Deadline: Sep. 09 (Mo), 23:59