Igor Poboiko: Selected topics in quantum mechanics

Date of publication: 12. 3. 2024
Mathematical physics seminar
15:15 - 17:45
Seminar room 133 (Jadranska Ulica 21, math building)

This mini-course will cover several selected topics in quantum mechanics. The first part will be focusing on adiabatic approximation and, including both non-stationary and stationary counterparts, latter also known as Born-Oppenheimer approximation. In the second part we will discuss the extension of the WKB semiclassical approximation to the complex plane, focusing on Stokes phenomenon, and apply it to the problem of over-the-barrier semiclassical reflection, linking it to the transition probability in the stationary adiabatic approximation. The third part will be focusing in great detail on the quantum tunneling problems in the path integral approach, including calculation of the functional determinants governing the behavior of pre-exponential factors by means of the Gelfand-Yaglom formalism. The last part will be devoted to the analysis of the one-dimensional Anderson localization using the Dorokhov-Mello-Pereyra-Kumar (DMPK) formalism.