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The Journal of Chemical Physics

Rigorous solutions of diatomic molecule oscillator with empirical potential function in phase space

Qian‐Shu Li, Jun Lu

Published Sep 15, 2000• 6 citations
Publisher

Abstract

Within the framework of the quantum phase-space representation established by Torres-Vega and Frederick, the rigorous solutions of the Schrödinger equation of the diatomic molecule oscillator with an empirical potential function are solved and discussed, and the Heisenberg uncertainty principle is interpreted in this physical system.
DOI
10.1063/1.1287282

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Within the framework of the quantum phase-space representation established by Torres-Vega and Frederick, the rigorous solutions of the Schrödinger equations of a particle in the δ potential fields are solved, and the Heisenberg uncertainty principle is interpreted in the phase space. Then it is found that, for the bound state of a particle in the δ potential well, the Wigner distribution function is the special result of the quantum phase-space probability density function with parameter k approaching infinity.
The rigorous solutions of the stationary Schrodinger equation for hydrogen atom are solved with the wave-mechanics method within the framework of the quantum phase-space representation established by Torres-Vega and Frederick. The Fourier-like projection transformations of wave function from the phase space to position and momentum spaces are extended to three-dimensional systems. The eigenfunctions in general position and momentum spaces could be obtained through the transformations from eigenfunction in the phase space.