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|
The lecture is given using black board.
|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|
|Class 15||Summary||Summarize your knowledge in QM.|
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