Exact solutions of a damped harmonic oscillator in a time dependent noncommutative space

Abstract

In this paper we have obtained the exact eigenstates of a two dimensional damped harmonic oscillator in time dependent noncommutative space. It has been observed that for some specific choices of the damping factor and the time dependent frequency of the oscillator, there exists interesting solutions of the time dependent noncommutative parameters following from the solutions of the Ermakov-Pinney equation. Further, these solutions enable us to get exact analytic forms for the phase which relates the eigenstates of the Hamiltonian with the eigenstates of the Lewis invariant. We then obtain expressions for the matrix elements of the coordinate operators raised to a finite arbitrary power. From these general results we then compute the expectation value of the Hamiltonian. The expectation values of the energy are found to vary with time for different solutions of the Ermakov-Pinney equation corresponding to different choices of the damping factor and the time dependent frequency of the oscillator.

arXiv comment28 pages Latex, Comments are welcome

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Cited by in corpus (5)

• A Path Integral Treatment of Time-dependent Dunkl Quantum Mechanics
• Exact solution of damped harmonic oscillator with a magnetic field in a time dependent noncommutative space
• Lewis and Berry phases for a gravitational wave interacting with a quantum harmonic oscillator
• The time-dependent quantum harmonic oscillator: a pedagogical approach via the Lewis-Riesenfeld dynamical invariant method
• Quantum harmonic oscillator in a time dependent noncommutative background