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 understand the Schroedinger's equation in the three-dimensional space, and will be able to:
* Explain the energy spectrum of a hydrogen atom and 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
|Intercultural skills||Communication skills||Specialist skills||Critical thinking skills||Practical and/or problem-solving skills|
Lecture and recitation are combined.
|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 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||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||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|
|Class 15||Summary||Summarize the contents of this course.|
Handouts are given out at the class
Evaluated by problem solving and written examination at the end of the course.
Students should have completed Introduction to Quantum Mechanics