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- School of Science
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School of Environment and Society
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- Common courses
- Liberal arts and basic science courses
- Academic unit or major
- Undergraduate major in Physics
- Instructor(s)
- Nishida Yusuke
- Class Format
- Lecture
- Media-enhanced courses
- Day/Period(Room No.)
- -
- Group
- -
- Course number
- PHY.Q208
- Credits
- 2
- Academic year
- 2024
- Offered quarter
- 4Q
- Syllabus updated
- 2024/3/14
- Lecture notes updated
- -
- Language used
- Japanese
- Access Index
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Course description and aims
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
Student learning outcomes
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 that will be developed
| ✔ Specialist skills | Intercultural skills | Communication skills | Critical thinking skills | Practical and/or problem-solving skills |
Class flow
Lectures with blackboard
Course schedule/Required learning
| Course schedule | Required learning | |
|---|---|---|
| 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. |
Out-of-Class Study Time (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.
Assessment criteria and methods
Evaluation based on reports and the final exam
Related courses
- PHY.Q207 ： Introduction to Quantum Mechanics
- PHY.Q218 ： Quantum Mechanics II（Exercise)
Prerequisites (i.e., required knowledge, skills, courses, etc.)
Students should have completed Introduction to Quantum Mechanics
