On nonstationary quadratic quantum systems
The unitary coupling between quadratic quantum systems, namely, a free particle with variable mass M ( t ), a particle with variable mass  in an alternating uniform field, and a harmonic oscillator with variable mass  and frequency w( t ) on which variable force acts is established by the method of evolution operator. The knowledge of the unitary coupling has allowed one to express easily in general form the propagators, invariants, wave functions, and other functions of the linear potential and the harmonic oscillator through the corresponding values for a free particle. The linear and quadratic invariants have been analyzed in ample details. From the obtained general results, the results well known in the literature follow as particular cases.