Time-dependent coherent squeezed states in a nonunitary approach

Abstract

In this work, we have applied the integrals of motion method in a nonunitary approach and so obtained the time-dependent displacement and squeezed parameters of the coherent squeezed states (CSS). On its turn, CSS for one-dimensional systems with general time-dependent quadratic Hamiltonian are constructed. We discuss the properties of these states, in particular, minimization of uncertainty relation and transition probabilities. As an application, we calculate the CSS of an oscillator with a time-dependent frequency and shown that the solution can be obtained from these well-known Mathieu's equation.