Physics 8210

Quantum Mechanics I

Syllabus 

Topics:

1. Preliminary definitions and background.
2. Postulates of quantum mechanics and their consequences—orthogonality, normalization, closure, expectation value, uncertainty principle, quantization of a system.
3. Correspondence principle and the Schröedinger equation—quasi-classical systems, time development operator.
4. One dimensional problems—time-independent problems, probability current, general properties of one-dimensional bound and unbound systems, harmonic oscillator, periodic potential, virtual binding.
5. Three dimensional problems—degeneracy, central forces, spherical harmonics, radial equation, free particle in spherical coordinates.
6. Scattering theory—partial wave analysis, phase shift, scattering by cut-off and long range Coulomb fields.
7. Perturbation theory for discrete states—non-degenerate, degenerate (special method), degenerate (general method).
8. Variation method.
9. Continuous spectra perturbation theory—Green’s functions, Born approximation for elastic scattering.
10. Time-dependent perturbation theory—general formulation, discrete-discrete transitions, discrete-continuum transitions.

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