Dr. Irina Petreska, Professor
Course content:
1. Historical development.
2. Wave function: Schrödinger's equation. Statistical interpretation. Probability. Rationing. Impulse. Uncertainty principle.
3. Time-independent Schrödinger equation: Stationary states. Continuity equation. Theorem of Ehrenfest. An infinitely deep potential pit. Harmonic Oscillator. A free particle. δ –potential pit. A symmetric rectangular potential well of finite depth. Kroning– Penny potential. Coefficient of transmission and reflection.
4. Formalism: Linear algebra. Spaces (functions like vectors, operators like linear transformations, Hilbert space). Dirac formalism. Matrices. Representations.
5. Generalized statistical interpretation: Uncertainty principle.
6. Quantum mechanics in three dimensions: Schrödinger equation in spherical coordinates. A hydrogen atom. A moment on impulse. Spin.
7. A charged particle in a magnetic field
8. A two-particle system. A planar and spatial rotator
9. Time-independent perturbation theory: Non-degenerate perturbation theory. Degenerate perturbation theory. Fine structure of the hydrogen atom. Time-dependent perturbation theory.
10. Variational principle: Theory. Ground state of a helium atom.
11. Quasi-classical (WKB) approximation.