Coherent States and Bloch Functions

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. [Russian Text Ignored.]