Week |
Subject |
Related Preparation |
1) |
Superposition principle. Normalization of finite function. Measurement in Quantum Mechanics. Expectation value. Uncertinity principle. |
|
2) |
Wave packets. Standing waves. Wave packets and uncertainity principle. Motion of the wave packets. |
|
3) |
Mathematical tools of Quantum Mechanics. Operators. Hermition adjoint. Projection operators. Commutator algebra. Uncertinity principle between two operators. Inverse and identical operators. Eigenvalues and eigenfunctions of operators. |
|
4) |
Dirac notation. Ket, Bra and definition of the operators in separated matrix presentation. Variation of the basic and unit transformations. Eigenvalue problem of matrix presentation. |
|
5) |
Definition of continuity principle. Notations of Momentum and position. Interrelations of momentum and position notations. Parity operators. |
|
6) |
Schrödinger equation. Stationary states. Time independent potential. Conservation of probability. Time dependent operators. Schrödinger equation and wave packets. Time dependency of expectation values. |
|
7) |
Solution of one dimensional Schrödinger equation. Square well with finite depth. Infinite square well. Single step potential. Barrier problems. Tunneling in a large barrier. |
|
8) |
Harmonic oscillator. Matrix presentation of various operators. Expectation values of various operators. |
|
9) |
Angular momentum. Orbital angular momentum. Matrix presentation of angular momentum. Geometric presentation of angular momentum. Schrödinger equation in spherical coordinates. Orbital and angular momentum operator. properties of spherical harmonics. |
|
10) |
Coulomb potential. General properties of radial wave for hydrogen atom. Complete Coulomb wavefunction. Hydrogen atom. Spherical symmetric solutions for hydrogen-like systems. Irreducible tensor operators. |
|
11) |
Time dependency of quantum states. Wave-packets states for free particle and dynamic particle. Energy-time uncertinity relation. |
|
12) |
Approximation methods for uniform states. Time-independent perturbation theory. Non-degenerate perturbation theory. |
|
13) |
Degenerate perturbation theory. Fine structure of hydrogen. Zeeman and Stark cases. Very fine splitting. High degrees in perturbation theory. |
|
14) |
Time-dependent perturbation theory. Adiabatic perturbation. Instant perturbation. |
|
Course Notes / Textbooks: |
Quantum Mechanics. Non-relativistic theory by L.D.Landau and E. M. Liftshitz |
References: |
1.L.Schiff Quantum Mechanics McGraw-Hill,1964,
2.J.Sakurai Modern Quantum Mechanics. Addison-Wesley Publishing Company ,1994
3.A.Messiah Quantum Mechanics. Dover Publications, 1999
4.N.Zettili Quantum Mechanics. Wiley,2008
5.E.Merzbacher Quantum Mechanics. Wiley,1998
6. R.Shankar Principles 0f Quantum Mechanics. Kluwer, 1994
7.C.Cohen-Tannoudji, B.Diu, F.Laloe Quantum Mechanics v.1 and 2, Wiley,1997 |