Regarding Nonstationary Quadratic Quantum Systems

Abstract

With the help of the evolution operator method, we have established unitary connection between quadratic systems, namely between a free particle with variable mass M(t) , a particle with variable mass M(t) in a variable homogeneous field, and a harmonic oscillator with variable mass M(t) and frequency ω(t) , on which a variable force F(t) acts. Knowledge of the unitary connection allowed us to express easily in general form the propagators, invariants, wave functions, and other functions of a linear potential and a harmonic oscillator in terms of the corresponding quantities for a free particle. We have analyzed the linear and quadratic invariants in detail. Results known in the literature follow as particular cases from the general results obtained here.