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Acta Physica Sinica

Exact wave function of the coupled harmonic oscillator with time-dependent mass and frequency

Ling Rui-liang, Feng Jin-fu, 常熟理工学院物理系,常熟 215500

Published Jan 1, 2009• 3 citations
Publisher

Abstract

Using the coordinate and momentum transformation theory and the trial function methed, the exact wave function of the coupled harmonic oscillator with time-dependent mass and frequency is derived.
DOI
10.7498/aps.58.2164

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In this work we present the classical and quantum solutions for an arbitrary system of time-dependent coupled harmonic oscillators, where the masses (m), frequencies (ω) and coupling parameter (k) are functions of time. To obtain the classical solutions, we use a coordinate and momentum transformations along with a canonical transformation to write the original Hamiltonian as the sum of two Hamiltonians of uncoupled harmonic oscillators with modified time-dependent frequencies and unitary masses. To obtain the exact quantum solutions we use a unitary transformation and the Lewis and Riesenfeld (LR) invariant method. The exact wave functions are obtained by solving the respective Milne–Pinney (MP) equation for each system. We obtain the solutions for the system with m1 = m2 = m0eγt, ω1 = ω01e-γt/2, ω2 = ω02e-γt/2 and k = k0.