An Alternative Model of the Damped Harmonic Oscillator Under the Influence of External Force

Abstract

In this paper we introduce the modified time-dependent damped harmonic oscillator. An exact solution of the wave function for both Schrödinger picture and coherent state representation are given. The linear and quadratic invariants are also discussed and the corresponding eigenvalues and eigenfunctions are calculated. The Hamiltonian is transformed to SU(1, 1) Lie algebra and an application to the generalized coherent state is discussed. It has been shown that when the system is under critical damping case the maximum squeezing is observed in the first quadrature F x . However, for the overcritical damping case the maximum squeezing occurs in the second quadrature F y . Also it has been shown that the system for both cases is sensitive to the variation in the coherent state phase.

Lewis and berry phases for a gravitational wave interacting with a quantum harmonic oscillator

“…The method involves using exact invariants to critically study these systems [13,14]. There have been numerous analyses involving the damping in a one dimensional quantum harmonic oscillator [15][16][17][18][19]. There also have been few studies involving damping in a two dimensional quantum harmonic oscillator [20] and later extended to noncommutative space [21].…”

“…where θ k (t) is a real function of time. Substituting equation (18) back in the time dependent Schrödinger equation given in equation (15), we obtain the following relation…”