Speciality:
01.01.04 (Geometry and topology)
Birth date:
08.02.1956
Keywords: theory of Group Representations and its applications to Quantum Mechanics; Spectral theory for the linear differential operators; N-variable analogues of the classical orthogonal polynomials.
Subject:
For two-dimensional Schrodinger operator H in periodic magnetic field $B(x,y)$ and electric field with periodic potential $V(x,y)$ are studied typical dispersion laws $\lambda_j(p_1, p_2)$ and their topological characteristics (quantum numbers) are established. The following theorem is proved: in general case, the Schrodinger operator possesses a countable set of dispersion laws with arbitrary quantum numbers which are no way related to each other or to the flux of the external magnetic field.
Main publications:
Lyskova A. S. Topologicheskie kharakteristiki operatora Shredingera v magnitnom pole i slabom potentsiale. // Teor. i matem. fizika, 1985, t. 65, # 3.
Lyskova A. S. Ortogonalnye mnogochleny neskolkikh peremennykh // DAN SSSR, 1991, t. 316, # 6, 1301–1306.
