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 |
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Lecture and recitation are combined.
Course schedule | Required learning | |
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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. |
Assign 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 Introduction to Quantum Mechanics