*A. Introduction and Review
1.Radiation: Particles and quantization of energy, photoelectric effect, Planck blackbody radiation, Compton effect
2. Particles: Waves and quantization of energy, Davisson-Germer experiment, particle diffraction
3. Optical spectroscopy: Bohr atom, Franck-Hertz experiment
B. Particle–Wave Representation
1. Wave Packets
2. Fourier integrals and delta functions: coordinate-momentum and frequency-time domains, Heisenberg uncertainty relations, operations representations
C. Wave Mechanics
1. Probability and state functions
2. Observables, operators, commutators and expectation values
3. Hilbert spaces and orthonormal vectors
4. Postulates of quantum mechanics
a. Schrodinger time dependent equation
b. Hermitian operators
c. Eigenvalues, eigenvectors
5. Conservation of probability density
6. Equation of motion and constants of motion
7. Seperation of space and time in Schrodinger time dependent equation; eigenfunctions and state functions
D. Matrix Mechanics
1. Orthonormal basis vectors and expansion
2. Representaion of linear operators
3. Eigenvalue problems and diagonalization
E. Applications
1. Step potentials
2. Finite potential barrier
3. Harmonic oscillator
4. Rigid rotor
5. Infinite potential well
*6. Finite potential well
*7. Multiple potential wells
F. Angular Momentum
1.Definition and commutator relations: raising and lowering operators
2. Spherical coordinates and eigenvalue problem: eigenvalues and eigenfunctions
3. Relation to magnetic moment
*4. Electron spin: Stern-Gerlock experiment, Pauli spin matrices, eigenvalues and eigenvectors
G. Hydrogen Atom
1. Eigenvalue problem and solution
2. Energy diagram and degeneracy
3. Wavefunctions, probability and expectation values
4. Spin and Pauli principle
*H. Approximation Method
1. Non-degenerate perturbation theory
2. Degenerate perturbation theory
3. Time dependent perturbation theory and transitions
*denotes optional topic
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