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Journal of Physics A Mathematical and General

Boson operators for generalised harmonic oscillators

Y Wang

Published Oct 1, 1987• 0 citations
Publisher

Abstract

A general treatment of generalised quantal harmonic oscillators with time-dependent mass, frequency, damping rate and driving forces is presented by using boson operators to find the quadratic invariant. Phase factor, eigenstates and state vectors are given. Examples of special cases are also given.
DOI
10.1088/0305-4470/20/14/018

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For a harmonic oscillator with time-dependent (positive) mass and frequency, a unitary operator is shown to transform the quantum states of the system to those of a harmonic oscillator system of unit mass and time-dependent frequency, as well as operators. For a driven harmonic oscillator, a unitary transformation which relates the driven system and a system of the same mass and frequency without a driving force is given, as a generalization of previous results, in terms of the solution of classical equation of motion of the driven system. Thus transformations give a simple way of finding exact wavefunctions of a driven harmonic oscillator system, provided the quantum states of the corresponding system of unit mass are given.