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Molecular Physics

A closed-form solution of the Schroedinger equation describing the harmonic oscillator with time dependent frequency and acted on by a time dependent perturbative force

Xavier Chapuisat, Jörn Manz

Published Dec 1, 1973• 15 citations
Publisher
DOI
10.1080/00268977300102761

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The problem of a quantal harmonic oscillator with damping and a time-dependent frequency acted on by a time-dependent perturbative force is exactly solved. The wavefunctions are found in Schrödinger representation using the theory of explicitly time-dependent invariants and also by an expansion of the Feynman propagator. The propagator is obtained in exactly closed form by an explicit path integration of the classical Lagrangian. It is found that the wavefunctions and the propagator depend only on the solution of classical damped oscillator through a single function ρ (t). The function ρ (t) itself may be obtained as a solution of a second order nonlinear differential equation under the appropriate set of initial conditions.