2024 Faculty Courses School of Science Undergraduate major in Physics
Quantum Mechanics II（Exercise) B
- Academic unit or major
- Undergraduate major in Physics
- Instructor(s)
- Kazuki Yamamoto / Kazuya Fujimoto / Yusuke Nishida
- Class Format
- Exercise (Face-to-face)
- Media-enhanced courses
- -
- Day of week/Period
(Classrooms) - 5-6 Tue / 5-6 Fri
- Class
- B
- Course Code
- PHY.Q218
- Number of credits
- 010
- Course offered
- 2024
- Offered quarter
- 4Q
- Syllabus updated
- Mar 17, 2025
- Language
- Japanese
Syllabus
Course overview and goals
This course is complementary to the lecture course (PHY.Q208). After passing this course, the students will be able to account for the basic concepts of quantum mechanics such as atomic model and angular momenta, and further be able to solve problems such as two- and three-dimensional harmonic oscillators, hydrogen atom, coupling of angular momenta, and approximate solutions of Schroedinger equation.
Course description and aims
The students will be able to solve Schroedinger equation for two- and three-diemensional harmonic oscillators and hydrogen atom, to perform angular momentum coupling, and to obtain approximate solutions by using perturbational and variational methods.
Keywords
Angular momenta, confluent hypergeometric functions, spherical harmonics, perturbation theory, and variational methods.
Competencies
- Specialist skills
- Intercultural skills
- Communication skills
- Critical thinking skills
- Practical and/or problem-solving skills
Class flow
A set of exercise problems will be given in every class session. The students are expected to solve all the problems by the next session. In class session, for each problem, a student will present how to solve it and field questions from the other students. The teacher will provide complementary explanation to the presentation.
Course schedule/Objectives
| Course schedule | Objectives | |
|---|---|---|
| Class 1 | Introduction | To review mathematical formulae. |
| Class 2 | Harmonic oscillators | To understand Hermite polynomials and further to solve Schrodinger equation for harmonic oscillators. |
| Class 3 | Angular momenta | To understand angular momenta, Legendre polynomials and related functions. |
| Class 4 | Spherical harmonics | To understand spherical harmonics and the algebraic structure of angular momentum operators. |
| Class 5 | Confluent hypergeometric functions | To understand Laguerre polynomials and associated Laguerre polynomials. |
| Class 6 | Hydrogen atom | To solve Schroedinger equation for electron in hydrogen atom. |
| Class 7 | Isotropic harmonic oscillators | To solver Schroedinger equation for isotropi two- and three-dimensional harmonic oscillators. |
| Class 8 | Dirac notation | To understand how to use Dirac's bra-ket notation. |
| Class 9 | Charged particle in magnetic field | To understand the characteristic behavior of electrons in magnetic filed, such as Landau levels, Zeeman splitting, and Aharonov-Bohm effect. |
| Class 10 | Spin angular momenta | To understand spin angular momenta. |
| Class 11 | Angular momentum coupling | To understand angular momentum coupling, and further to solve problems with spin-spin interaction and spin-orbit interaction. |
| Class 12 | Perturbation theory, part 1 | To solve problems by using perturbation theory for non-degenerated systems. |
| Class 13 | Perturbation theory, part 2 | To solve problems by using perturbation theory for degenerated systems. |
| Class 14 | Selection rule in optical transition | To solve problems by using perturbation theory for time-dependent systems and to understand selection rule for electric dipole transition. |
Study advice (preparation and review)
To enhance learning, students are encouraged to spend approximately 100 minutes preparing for class and another 100 minutes reviewing class content afterwards for each class.
Textbook(s)
Same as those used in the lecture course (PHY.Q208).
Reference books, course materials, etc.
L.I. Schiff, "Quantum Mechanics" (McGraw-Hill College)
Evaluation methods and criteria
Evaluated based on presentations and reports.
Related courses
- PHY.Q208 ： Quantum Mechanics II(Lecture)
- ZUB.Q206 ： Quantum Mechanics II
Prerequisites
Nothing.