||Reference Textboks: Modern Quantum Mechanics by J. J. Sakurai
Quantum Mechanics by D. J. Griffiths
1. Linear Vector Spaces, Concept of Inner Product,
Dual Space, Dirac Notation, Gram-Schmidt orthogonalization,
Linear Operators and their matrix representation, projection operator,
Brief Discussion of orthogonal, Hermitian and unitary matrices,
eigenvalue problem, normal matrices and their
spectral decomposition, Hilbert Space and square
integrable functions, Dirac delta-function.
2. Postulates of Quantum Mechanics, meaning of wave function
(Copenhagen Interpretation), Uncertainty principle,
Heisenberg microscope, measurement of physics observables,
compatible and incompatible observables, Real space
representation of Schroedinger`s equation.
3. One dimensional problems: Brief review of infinite
and finite potential wells. Potential barrier and
tunneling. Scattering off step potential.
4. 1-d Harmonic Oscillator, Hermite polynomials, minimal
uncertainty product, number representation.
5. Symmetries and their generators, translational
invariance and linear momentum, Discrete symmetries (Parity)
6. Rotational Symmetry and angular momentum, angular
momentum algebra, coordinate representation of L^2 and L_z
and their eigenfunctions (spherical harmonics),
Addition of Angular Momenta, Clebsch-Gordon Coefficients,
7. Stern-Gerlach experiment, spin-1/2 representation and
interaction of spin with magnetic field.
8. Solution of Schroedinger`s equation for central
potentials, Hydrogen atomp problem (Laguerre polynomials)
9. Introduction to stationary state perturbation theory
(non-degenerate and degenerate), Calculation of scattering
amplitudes for simple potentials.
The total number of lectures in parantheses add up to 28.