2024 Faculty Courses School of Science Undergraduate major in Physics
Quantum Mechanics II（Lecture)
- Academic unit or major
- Undergraduate major in Physics
- Instructor(s)
- Yusuke Nishida
- Class Format
- Lecture (Face-to-face)
- Media-enhanced courses
- -
- Day of week/Period
(Classrooms) - 3-4 Tue / 3-4 Fri
- Class
- -
- Course Code
- PHY.Q208
- Number of credits
- 200
- Course offered
- 2024
- Offered quarter
- 4Q
- Syllabus updated
- Mar 17, 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 equation in the three-dimensional space, and will be able to explain the energy spectrum of a hydrogen atom and apply variational and perturbative methods.
Keywords
Schroedinger 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
Lectures with blackboard
Course schedule/Objectives
| Course schedule | Objectives | |
|---|---|---|
| Class 1 | Schroedinger 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 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 by referring to textbooks and other course material.
Textbook(s)
Lecture notes will be distributed via T2SCHOLA.
Reference books, course materials, etc.
Textbooks specified by the instructor.
Evaluation methods and criteria
Evaluation based on reports and the final exam
Related courses
- PHY.Q207 ： Introduction to Quantum Mechanics
- PHY.Q218 ： Quantum Mechanics II（Exercise)
Prerequisites
Students should have completed Introduction to Quantum Mechanics