Approximate methods in quantum mechanics; introduction to scattering theory.
Course Prerequisites
See presentation of the full course
Teaching Methods
Lectures during which the calculations and approximations are shown in detail at the balackboard, and classroom exercises, where the solution of problems of Quantum Mechanics is shown and discussed in detail.
Assessment Methods
Written examination consisting in the solution of problems of quantum mechanics; who passes the written exam can take on the oral examination, during which an item treated in Mod. B will be discussed (after an analogous discussion of an item treated in Mod. A).
Texts
D.J. Griffiths, Introduction to Quantum Mechanics; J.J. Sakurai, J. Napolitano, Meccanica quantistica moderna.
Contents
Time evolutioin pictures: Schroedinger, Heisenberg, Interaction. The time evolution operator for time-dependent hamiltonians: Dyson expansion. Non-degenerate and degnerate time-independent perturbation theory. Some perturbative hamiltonians: the relativistic correction, the Zeeman effect, the spin-orbit hamiltonian, the hyperfine splitting hamiltonian. Perturbative treatment of time evolution: transition and survival probabilities. Time-dependent perturbation theory: constant and sinusoidal perturbations. Emission and absorption of radiation. Spontaneous emission. Einstein’s coefficients. Non-perturbative approximate methods: the variational method; WKB; Hartree; Hartree-Fock (elements). Elementary scattering theory: classical vs quantum treatment, the scattering cross section. Partial wave expansion; phase shifts; Argand diagram; the optical theorem; the Breit-Wigner approximation; the Born approximation; Green’s functions. Irreducible tensorial sets: definition and examples; the Wigner-Eckart theorem; selection rules. Path integral quantization (elements). The adiabatic theorem. The Aharonov-Bohm effect.
Course Language
Italian
More information
All students who are entitled to benefit from the inclusive teaching methods (see portale.unipv.it/it/didattica/servizi-lo-studente/modalita-didattiche-inclusive) will be given access to the lecture notes and to the videos available on KIRO. Furthermore, they are cordially invited to contact the chair of the course to set up online meetings or group activities.
