Premium
Coherent States and Bloch Functions
Author(s) -
Krivoshlykov S. G.,
Manko V. I.
Publication year - 1980
Publication title -
physica status solidi (b)
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.51
H-Index - 109
eISSN - 1521-3951
pISSN - 0370-1972
DOI - 10.1002/pssb.2220970106
Subject(s) - physics , constant (computer programming) , classical mechanics , momentum (technical analysis) , motion (physics) , electromagnetic field , electron , coherent states , magnetic field , representation (politics) , field (mathematics) , quantum mechanics , mathematical physics , mathematical analysis , quantum , mathematics , pure mathematics , finance , politics , computer science , political science , law , economics , programming language
Abstract A quasi‐momentum representation for an arbitrary quantum system is constructed by the integrals‐of‐motion method and by the coherent‐states method. Explicit expressions in terms of the Jakobi ϑ‐functions are obtained for the Bloch functions of the following dynamical systems: a relativistic and non‐relativistic electron moving in a constant uniform magnetic field and a non‐relativistic electron moving in both, time‐dependent and constant crossed electromagnetic fields. New mathematical relations between the Jacobi ϑ‐functions are obtained.