Advanced Studies in Quantum Mechanics I

General Foundation

The course is also offered to exchange programme students.

With the succesfull completion of the course, the students will: - will handle with ease the formalism of orbital angular momentum and will be able to solve problems in three dimensions with central potentials, like the hydrogen atom. - will be able to able to solve scattering problems with central potentials (calculate phase shifts, cross sections). - will be able to use the perturbation method to solve problems, in both the time-independent and the time-depependent perturbations. - will have understood that the matrix element defines selection rules, that the spontaneous emission happens only because the EM filed is quantised, and they will be able to calculate transition rates. - and in general, they will have mastered the theory and will be able to solve problems in non-relativistic quantum mechanics

- Bound states in one-dimensional potential wells. Scattering of plane waves from one-dimensional potential wells and steps. Calculation of transmission coefficients with the use of transfer matrices. - Harmonic oscillator. Eigenvalues and energy levels with the use of raising and lowering operators. - Angular momentum. Eigenvalues and eigenstates of the operators L^2, Lz, L+ and L- - Systems in three dimensions - Rotations and addition of angular momenta - Scattering and cross section. Scattering of spinless particles. Born approximation. - Time-independent perturbations: - Perturbation method for non-degenerate and for degenerate states. - The "real hydgrogen atom" (spin-orbit coupling, relativistic corrections, anomalous Zeeman effect). - Time-dependent perturbations: - Pictures of Quantum Mechanics and time evolution of a system. Transition probability, in general and for a constant perturbation. Transition rate and Fermi's golden rule. - Transition probability for a harmonic perturbation (forced absorption and emision). Transitions in the Adiabatic and the sudden approximations. - Transition probability in first-order approximation in Schoroedinger's picture. martix element and selection rules. - Interaction of ElecrtoMagnetic radiation with an atom: with the classical approximation of the ElectroMagnetic radiation (waves) and with the quantized EM radiation (photons). - Spontaneous de-excitation: exponential decay of the probability to remain in en excited state. - Density of states and phase-space.

06-06-2019