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Two Wave Interpretation of the 2-Dimensional Harmonic Oscillator

Huang Chun

Published Jan 1, 1999• 0 citations
OpenAlex

Abstract

The 2 dimensional harmonic oscillator is studied by means of two wave interpretation quantum theory. The time evolution equation and some constants of the motion describing the single 2 dimensional harmonic oscillator and the classical limits are obtained. The relations between the two wave quantum theory and the single wave quantum theory are discussed.

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Physical Review•Nov 5, 1968•74 citations
The 2 dimensional harmonic oscillator is studied by means of two wave interpretation quantum theory. The time evolution equation and some constants of the motion describing the single 2 dimensional harmonic oscillator and the classical limits are obtained. The relations between the two wave quantum theory and the single wave quantum theory are discussed.
Systems of interacting harmonic oscillators have recently received considerable attention as models for describing a variety of physical problems. We have investigated the validity of the rotating-wave approximation which constitutes the traditional approach to the solution of the dynamical problem by comparing it with the exact solution. A numerical comparison has been made and the limits of validity of the rotating-wave approximation has been established in terms of the strength of oscillator interaction.In particular, the time development of dynamical operators and certain transition probabilities have been compared. In the region where the rotating-wave approximation is valid, the time evolution of the quasiprobability distribution $P(\ensuremath{\alpha}, t)$ of one oscillator is given for several initial conditions. A counting scheme similar to the argument given by Feynman for the driven harmonic oscillator, is proposed for the interpretation of the time-dependent transition amplitudes between number states.