Solvability in 2-dim Quantum Mechanics: SUSY separation of variables

by Prof. Mikhail V. Ioffe (Saint-Petersburg State University, Russia)

Friday 5 Jul 2013, 11:00 → 12:00 Europe/Rome

Aula teorici (DIFA)

The supersymmetrical approach in Quantum Mechanics and a few its generalizations are reviewed very briefly. More attention is given to 2-dim generalization of Polynomial SUSY Quantum Mechanics. Two different approaches are formulated to analyze two-dimensional quantum models which are not amenable to standard separation of variables. Both methods are essentially based on SUSY intertwining relations. The first one explores the opportunity to separate variables in the supercharge, and it gives a part of spectrum of the Schrodinger Hamiltonian. The second method works when the superpartner Hamiltonian allows the standard separation of variables. Then the whole spectrum and wave functions of initial Hamiltonian can be found. Both methods are illustrated by the example of two-dimensional generalization of Morse potential.

Slides Ioffe_July_2013.pdf