Exactly Soluble Harmonic Oscillator for a Particular Form of Time and Coordinates-Dependent Mass

An exact solution of Schrodinger equation is presented for the problem of a harmonic oscillator of mass varying with time and coordinates according to \begin{aligned} m(q,t)=m_{0}/\text{e}^{-\nu t}-k_{0}^{2}q^{2}. \end{aligned} This case, compared with known types of equivalent interactions, leads again to a new one that relates the damped harmonic oscillator with velocity-depentent interaction problem.