Course title
応用物理数学   [Advanced Mathematical Physics]
Course category	common courses	Requirement		Credit	2
Department		Year	～	Semester	3rd
Course type	3rd	Course code	1060489
Instructor(s)
生嶋 健司, 森下 義隆   [IKUSHIMA Kenji, MORISHITA Yoshitaka]
Facility affiliation	Faculty of Engineering	Office	afjgxte/L1151	Email address

Course description

Symmetry is an indispensable concept in physics. In all fields such as elementary particles, the universe, atoms and molecules, solid physics, and physics of continuum, symmetry always comes out. In this lecture, we introduce the basics of group theory, which is mathematics for describing the concept of symmetry, and apply it to concrete physical systems. Goal: (1) Master the basics of mathematics (group theory) that describes the concept of symmetry. (2) Review crystallography, quantum mechanics, molecular / lattice vibration, band theory, tensor amount, etc. from the point of view of symmetry. This subject is one of the required compulsory subjects.

Expected Learning

1) To understand and explain mathematical concepts (group theory) expressing symmetry. 2) Classification of solid crystals from the viewpoint of symmetry. 3) To be able to classify quantum mechanical problems from the viewpoint of symmetry. 4) To understand and explain the relation between the symmetry of crystals and the symmetry of physical property parameters. View the diploma policy of this subject: Please refer to the curriculum map of the course guidance.

Course schedule

1. Introduction Symmetry and physics --- space symmetry, time reversal symmetry Bravais lattice and crystal system How to proceed with class 2. Point group 3. Space group 4. Definition of group theory 5. Recombination Theorem (Reordering Theorem) 6. Group representation (matrix representation) 7. Irreducible expressions and character table 8. Irreducible and direct product 9. Applications to quantum mechanics--basis function, overlap integral 10. Applications to Quantum Mechanics-cegeneration, Parity, Selection Rule 11. Applications to Solid-State Physics-Translational Symmetry and Electronic States (Bloch's Theorem and Band Theory) 12. Applications to Solid-State Physics-Translational Symmetry and Lattice Vibration 13. Tensor 14. Tensor and Macroscopic Physical Property Parameter 15. Summary

Prerequisites

In addition to 30 hours that students spend in the class, students are recommended to prepare for and revise the lectures, spending the standard amount of time as specified by the University and using the lecture handouts as well as the references specified below.

Required Text(s) and Materials

References

「物質の対称性と群論」今野豊彦　著　共立出版 「応用群論」犬井鉄郎、田辺行人、小野寺嘉孝　著　裳華房 "Modern Quantum Mechanics" J. J. Sakurai Addison Wesley Longman

Assessment/Grading

Reports 100%

Message from instructor(s)

Course keywords

Office hours

From 11:00 to 13:00. Email questions are possible.

Remarks 1

Remarks 2

Related URL

Lecture Language

Japanese

Language Subject

Last update

3/1/2021 5:48:21 PM