Madelung representation of damped parametric quantum oscillator and exactly solvable Schrödinger-Burgers equations

摘要: We construct a Madelung fluid model with time variable parameters as dissipative quantum and linearize it in terms of Schrodinger equation time-dependent parameters. It allows us to find exact solutions the nonlinear system corresponding classical linear ordinary differential frequency damping. For complex velocity field, takes form Schrodinger–Burgers equation, for which we obtain using Cole–Hopf transformation. In particular, give results systems related Caldirola–Kanai-type harmonic oscillator. Collapse wave function models possible implications cosmology are discussed.