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- Academic unit or major
- Physics
- Instructor(s)
- Toyoda Masayuki Fujimoto Kazuya Jido Daisuke
- Class Format
- Exercise (Face-to-face)
- Media-enhanced courses
- Day/Period(Room No.)
- Tue5-6(H116) Fri5-6(H116)
- Group
- -
- Course number
- ZUB.Q218
- Credits
- 2
- Academic year
- 2022
- Offered quarter
- 4Q
- Syllabus updated
- 2022/4/20
- Lecture notes updated
- -
- Language used
- Japanese
- Access Index
-
Course description and aims
This course is complementary to the lecture course (ZUB.Q206). 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.
Student learning outcomes
The students will be able:
(1) to solve Schroedinger equation for two- and three-diemensional harmonic oscillators and hydrogen atom,
(2) to perform angular momentum coupling, and
(3) to obtain approximate solutions by using perturbational and variational methods.
Keywords
Schroedinger's equation, angular momentum, spin, hydrogen atom, Zeeman effect, fine structure, variational method, perturbation theory
Competencies that will be developed
| ✔ 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/Required learning
| Course schedule | Required learning | |
|---|---|---|
| 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. |
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.
They should do so by referring to textbooks and other course material.
Textbook(s)
Same as the lecture course (ZUB.Q206)
Reference books, course materials, etc.
L.I. Schiff, "Quantum Mechanics" (McGraw-Hill College)
Assessment criteria and methods
Evaluated based on presentaions and reports.
Related courses
- ZUB.Q206 ： Quantum Mechanics II
Prerequisites (i.e., required knowledge, skills, courses, etc.)
Enrollment in Quantum Mechanics II (ZUB.Q206) is strongly recommended.
