2023 Faculty Courses School of Science Undergraduate major in Physics
Quantum Mechanics II（Lecture)
- Academic unit or major
- Undergraduate major in Physics
- Instructor(s)
- Daisuke Jido
- Class Format
- Lecture (Face-to-face)
- Media-enhanced courses
- -
- Day of week/Period
(Classrooms) - 3-4 Tue (S2-203(S222)) / 3-4 Fri (S2-203(S222))
- Class
- -
- Course Code
- PHY.Q208
- Number of credits
- 200
- Course offered
- 2023
- Offered quarter
- 4Q
- Syllabus updated
- Jul 8, 2025
- Language
- Japanese
Syllabus
Course overview and goals
This course covers quantum mechanical treatment of the following topics.
* particle motion in central force
* charged particles in background magnetic field
* variational and perturbation theory
Course description and aims
At the end of this course, students will understand the Schroedinger's equation in the three-dimensional space, and will be able to:
* Explain the energy spectrum of a hydrogen atom and by using Schroedinger's equation.
* Apply variational and perturbative methods.
Keywords
Schroedinger's equation, angular momentum, spin, hydrogen atom, Zeeman effect, fine structure, perturbation, variational methods
Competencies
- Specialist skills
- Intercultural skills
- Communication skills
- Critical thinking skills
- Practical and/or problem-solving skills
Class flow
Lecture notes are distributed in advance. The lectures are given by writing on the blackboard and with slides. The lecture notes and the slides are open in T2SCHOLA.
Course schedule/Objectives
| Course schedule | Objectives | |
|---|---|---|
| Class 1 | Schroedinger's equation in thee-dimensional space | Understand a derivation of the energy spectrum of a particle in a box. |
| Class 2 | spherical harmonics | Separate out the angular variables and drive spherical harmonics |
| Class 3 | angular momentum | Understand the definition of the angular momentum and the commutation relations among its components. |
| Class 4 | wave equation for radial direction | Understand the energy spectrum of a particle in a spherical square well potential |
| Class 5 | hydrogen atom | Derive the energy spectrum of a hydrogen atom. |
| Class 6 | angular momentum algebra | Construct the eigenstates from the commutation relations |
| Class 7 | Spin | Understand the similarity and the difference between spin and orbital angular momentum. |
| Class 8 | product of angular momenta | Explain the product of two angular momenta. |
| Class 9 | motions in electromagnetic fields | Understand the interaction between charged particles and background electromagnetic fields. |
| Class 10 | fine structure | Explain the fine structures of hydrogen atom. |
| Class 11 | time independent perturbation theory for nondegenerate case | Apply the time independent perturbation theory for nondegenerate systems |
| Class 12 | time independent perturbation theory for degenerate case | Apply the time independent perturbation theory for degenerate systems |
| Class 13 | time dependent perturbation theory | Apply the time dependent perturbation theory |
| Class 14 | variational method | Apply the variational method |
Study advice (preparation and review)
To enhance the effectiveness of 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 by referring to textbooks and other course material.
Textbook(s)
Assign later
Reference books, course materials, etc.
Handouts are given out at the class
Evaluation methods and criteria
Evaluated by problem solving and written examination at the end of the course.
Related courses
- PHY.Q207 ： Introduction to Quantum Mechanics
Prerequisites
Students should have completed Introduction to Quantum Mechanics