Using the evolution operator method to describe a particle in a homogeneous alternating field

Using the evolution operator method, we construct coherent states of a nonrelativistic free particle with a variable mass $M(t)$ and a nonrelativistic particle with a variable mass $M(t)$ in a homogeneous alternating field. Under certain physical conditions, they can be regarded as semiclassical states of particles. We discuss the properties (in particular, the completeness relation, the minimization of the uncertainty relations, and the time evolution of the corresponding probability density) of the found coherent states in detail. We also construct exact wave functions of the oscillator type and of the plane-wave type for the considered systems and compute the quantum Wigner distribution functions for the wave functions of coherent and oscillator states. We establish the unitary equivalence of the problems of a free particle and a particle in a homogeneous alternating field.