Quantum Mechanics (Phys 453)

Course Level :  7
Credit hours: 4 ( 3+1)
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1) Introduction and Revision  :
Revision of classical Hamiltonian dynamics, Poisson brackets and phase space.
Quantisation of Hamiltonian systems, the postulates of quantum mechanics and Hilbert space.
2) Mathmatical background
Bra-Ket notation and the superposition principle, the spectral theorem. Linear operators and eigenvalues. Descrete and contiuous spectra . Functions of the space L 2 .
3) Stationary states
Theory of saperaton of variables in Scrödinger'sequation, infinite well, , finite well and other scattering problems in 1 dimention. The quantum harmonic oscillator.
4) Problems in 3 dimentions
The quantisation of angular momentum , the  simple hydrogen atom
5) Spin
The spin of an electron, pauli matrices and their mathmatical properties. The magnatic dipole moment of the electron .
6) Addition of angular momenta
L-S coupling , and the angular momentum J = L+S. J-J adition ., and the clebsch gordan coefficients.
The real hydrogen atom 7).
Spin -orbit interaction in hydrogen, other terms affecting the fine structure . The hyper fine structure and the nuclear spin
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Refrences :
- Griffiths, D. J., & Harris, E. G. (1995). Introduction to quantum mechanics. American Journal of Physics, 63(8), 767-768.
Tannoudji, C. C., Bernard, D., & Franck, L. (1973). Mécanique quantique. Tome I. et Tome II
Alsaleh, Salwa " Lecture Notes in Quantum Mechanics" 2017 :