2026 (Current Year) Faculty Courses School of Science Department of Physics Graduate major in Physics
Quantum Theory of Electrons in Solids
- Academic unit or major
- Graduate major in Physics
- Instructor(s)
- Hiroaki Ishizuka
- Class Format
- Lecture
- Media-enhanced courses
- -
- Day of week/Period
(Classrooms) - Class
- -
- Course Code
- PHY.C450
- Number of credits
- 200
- Course offered
- 2026
- Offered quarter
- 3Q
- Syllabus updated
- Jul 16, 2026
- Language
- English
Syllabus
Course overview and goals
Solids are quantum many-body systems composed of electrons and atomic nuclei which, despite the simplicity of their constituents, exhibit a remarkably rich variety of phenomena including superconductivity, magnetism, and topological phases of matter. This course provides a systematic introduction to the theoretical framework for describing electrons in solids. Beginning with the Born–Oppenheimer approximation, the course covers mean-field approaches — including the Hartree and Hartree–Fock methods and the variational principle — before proceeding to many-body perturbation theory formulated in terms of Green's functions, self-energy, and the Dyson equation. The overarching goal is to develop a quantitative understanding of electronic properties of solids grounded in the quasiparticle picture.
Course description and aims
Through this course, students will learn:
- Basic concepts to understand the electronic properties of the solid
- Quasiparticles
- Calculations using Green's function
Keywords
Energy Bands, Quasiparticle, electron gas, Green's function
Competencies
- Specialist skills
- Intercultural skills
- Communication skills
- Critical thinking skills
- Practical and/or problem-solving skills
Class flow
Before coming to class, students should read the course schedule and check what topics will be covered.
Course schedule/Objectives
| Course schedule | Objectives | |
|---|---|---|
| Class 1 | Born-Oppenheimer approximation and Hamiltonian in solids |
Introduce quantum mechanical Hamiltonian for electrons in solids |
| Class 2 | Hartree approximation |
Understand the physical background of Hartree approximation |
| Class 3 | Hartree-Fock approximation |
Understand the variational principle and approximations based on the variational principle. |
| Class 4 | Jellium model and homogeneous electron gas |
Apply various approximations to homogeneous electron gas. |
| Class 5 | electron correlation |
Understand the limit of the Hartree-Fock approximation. |
| Class 6 | Quantum Monte Carlo method |
Introduce the method beyond the Hartree-Fock approximation. |
| Class 7 | Enegy bands in solids and quasiparticles |
Understand why many-electron systems in solids show the band structure. |
| Class 8 | Green's function |
Introduce Green's function |
| Class 9 | Dyson's equation and self-energy operator |
Understand how to calculate Green's function. |
| Class 10 | Quasiparticle equation |
Redefine energy bands in solids using Green's function. |
| Class 11 | Non-equilibrium Green function |
Understand the basic concepts of non-equilibrium Green's function |
| Class 12 | Kinetic equation |
Understand the Kinetic equations of non-equilibrium Green's function |
| Class 13 | Boltzmann limit |
Understand how to calculate the transport coefficients in the Boltzmann limit |
| Class 14 | Transport phenomena 1 |
Understand the electron transport in solids. |
| Class 15 | Transport phenomena 2 |
Understand the electron transport in solids. |
Study advice (preparation and review)
To enhance effective learning, students are encouraged to spend approximately 100 minutes preparing for class and another 100 minutes reviewing class content afterwards (including assignments) for each class.
They should do so by referring to textbooks and other course material.
Textbook(s)
None
Reference books, course materials, etc.
To be introduced in the lecture.
Evaluation methods and criteria
To be evaluated by exams.
Related courses
- PHY.Q438 ： Quantum Mechanics of Many-Body Systems
Prerequisites
No prerequisites. However, this course assumes the students are familiar with
- Undergraduate-level quantum mechanics, statistical mechanics, and physical mathematics
- Topics taught in Quantum Mechanics of Many-Body Systems (PHY.Q438)