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2023　Quantum Theory of Electrons in Solids

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Academic unit or major
Graduate major in Physics
Instructor(s)
Ishizuka Hiroaki 
Class Format
Lecture    (Face-to-face)
Media-enhanced courses
Day/Period(Room No.)
Mon1-2(M-B107(H104))  Thr1-2(M-B107(H104))  
Group
-
Course number
PHY.C450
Credits
2
Academic year
2023
Offered quarter
3Q
Syllabus updated
2023/9/28
Lecture notes updated
-
Language used
English
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Course description and aims

This course focuses on the electronic properties of solids, especially quantum mechanical properties. Solid is a many-body system consisting of electrons and nuclei. Despite only two ingredients, the electrons in solid show rich states and physical properties. In this course, we learn basic concepts and theoretical methods to study the electronic states in the solid.

Student learning outcomes

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 that will be developed

✔ 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/Required learning

  Course schedule Required learning
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.

Out-of-Class Study Time (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.

Assessment criteria and methods

To be evaluated by exams.

Related courses

  • PHY.Q438 ： Quantum Mechanics of Many-Body Systems

Prerequisites (i.e., required knowledge, skills, courses, etc.)

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)

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