2016 | Quantum Theory of Electrons in Solids

2016　Quantum Theory of Electrons in Solids

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Academic unit or major: Graduate major in Physics

Instructor(s): Saito Susumu

Class Format: Lecture

Media-enhanced courses

Day/Period(Room No.): Mon1-2(H115) Thr1-2(H115)

Group: -

Course number: PHY.C450

Credits: 2

Academic year: 2016

Offered quarter: 3Q

Syllabus updated: 2016/4/27

Lecture notes updated: -

Language used: Japanese

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Syllabus

Course description and aims

This course focuses on the electronic properties of solids, especially the quantum mechanical properties. A few methods based on the quantum many-body theory will be discussed from the viewpoint of quantitative description of real materials. Results of these theories will be compared with the experimental results.

Student learning outcomes

Students will learn how interacting electrons in condensed matter show different properties based on the quantum mechanics. They will understand:
1) Energy bands in solids
2) Homogeneous electron gas
3) Hartree approximation
4) Hartree-Fock approximation
5) Electron correlation
6) Density-Functional Theory

Keywords

Energy Bands, Quasiparticle, electron gas, Density-Functional Theory, Local-Density Approximation

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	Introduction to Density-Functional Theory	Understand the basic concept of the Density-Functional Theory.
Class 12	Local Density Approximation	Understand the Local Density approximation, the most popular method in the Density-Functional Theory.
Class 13	Application of DFT to various solids	Understand the accuracy of the Density-Functional Theory in various solids.
Class 14	Linear Response and density-density response function	Introduce the density-density response function.
Class 15	Density-Functional Theory for excited states	Understand how the excited states in solids can be given within the framework of the Density Functional theory.

Textbook(s)

To be introduced in the lecture.

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 special prerequisites.

TOKYO INSTITUTE OF TECHNOLOGY