Maslov’s asymptotic methods in problems of the theory of optical lattices

Application of Maslov’s asymptotic methods to equations that arise in the theory of optical lattices was considered. The occurrence of a small parameter in the Schrödinger equations with potentials of three-dimensional and controlled optical lattice was investigated and the conditions of application of Maslov’s asymptotic methods for solving these equations was determined. Consideration of different conditions imposed on the parameters in these potentials led to the use of two different methods for solving the arising equations: Maslov’s method of a complex germ and Maslov’s operator-valued method of a complex germ. Expressions that can be used to calculate the desired characteristics of the atomic systems under consideration in optical lattices were derived.