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理论物理通讯：英文版

Variable Frequency Harmonic Oscillator in an Electromagnetic Field

Bo Huang

Published Jan 1, 2004• 0 citations
OpenAlex

Abstract

The invariant,propagator,and wavefunction for a variable frequency harmonic oscillator in an electro- magnetic field are obtained by making a specific coordinate transformation and by using the method of phase space path integral method.The probability amplitudes for a dissipative harmonic oscillator in the time varying electric field E(t)=E_0 sin(Ωt) are obtained.

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•Jan 1, 2006•6 citations
The invariant,propagator,and wavefunction for a variable frequency harmonic oscillator in an electro- magnetic field are obtained by making a specific coordinate transformation and by using the method of phase space path integral method.The probability amplitudes for a dissipative harmonic oscillator in the time varying electric field E(t)=E_0 sin(Ωt) are obtained.
The exact solutions to the time-dependent Schrodinger equation for a harmonic oscillator with time-dependent mass and frequency were derived in a general form. The quantum mechanical propagator was calculated by the Feynman path integral method, while the wave function was derived from the spectral representation of the obtained propagator. It was shown that the propagator and the wave function depended on the s solution of a classical oscillator, in which the amplitude and phase satisfied the auxiliary equations. To demonstrate the derivation of the solution from our auxiliary equations, exponential and periodic functions of mass with constant frequency were imposed to evaluate the propagator and wave function for the Caldirola-Kanai and pulsating mass oscillators, respectively.