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
At the end of this course, students will be able to:
* Explain the energy spectrum of a hydrogen atom and its behavior in a background magnetic field by using Schroedinger's equation.
* Apply variational and perturbative methods.
Schroedinger's equation, angular momentum, spin, hydrogen atom, Zeeman effect, fine structure, perturbation, variational methods
✔ Specialist skills | Intercultural skills | Communication skills | Critical thinking skills | Practical and/or problem-solving skills |
Lecture notes are distributed in advance. The lectures are given with slides. The lecture notes and the slides are open in OCW-i.
Course schedule | Required learning | |
---|---|---|
Class 1 | Schroedinger's equation in thee-dimensional space | Understand a derivation of the energy spectrum of a particle in a cuboid. |
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 | motions in electromagnetic fields | Understand the interaction between charged particles and background electromagnetic fields. |
Class 9 | product of angular momenta | Explain the product of two angular momenta. |
Class 10 | fune 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 | Understand the variational method |
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.
Assigned later
Handouts are given out at the class
Evaluated by problem solving and written examination at the end of the course.
Students should have completed Quantum Mechanics I