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
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 | motion in central force | Derive the Schroedinger equation in the spherical coordinate system. |
Class 3 | angular momentum | Understand the definition of the angular momentum and the commutation relations among its compinents. |
Class 4 | spherical harmonics | Understand the relation between particle motion on a sphere and spherical harmonics. |
Class 5 | Hydrogen atom | Derive the energy spectrum of a hydrogen atom. |
Class 6 | Motions in magnetic fields | Understand the interaction between charged particles and background magnetic fields. |
Class 7 | Spin | Understand the similarity and the difference between spin and orbital angular momentum. |
Class 8 | Midterm exam to assess the students’ level of understanding on what has been taught so far and explanation of solutions | None |
Class 9 | Rotation and angular momentum | Confirm that the angular momentum generates rotations. |
Class 10 | Fine structure | Explain the fine structures of hydrogen atom. |
Class 11 | Variational method | Apply the variational method. |
Class 12 | Time independent perturbation theory | Apply the time independent perturbation theory |
Class 13 | Time dependent perturbation theory | Apply the time dependent perturbation theory |
Class 14 | Product of angular momenta | Explain the product of two angular momenta. |
Class 15 | Summary | Summarize the contents of this course. |
Assign later
Assign later
Evaluated by a midterm and final exams.
Students should have completed Introduction to Quantum Mechanics