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Il Nuovo cimento della Società italiana di fisica. B/Il Nuovo cimento B

Generalized phase-space distributions associated with a pseudo-oscillator

G. S. Agarwal

Published Feb 1, 1970• 3 citations
Publisher
DOI
10.1007/bf02711200

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Abstract The main objective of this research paper is to develop an approach within phase-space quantum mechanics for the pseudo-harmonic oscillator potential, enabling the derivation of analytical expressions for the Wigner distribution function and the formulation of a general expression for the moments associated with higher-order position and momentum operators. This approach also allows for the identification of a key dimensionless parameter α in the phase-space transformations. This parameter contributes to improving the general analytical expression for the energy levels. These energy levels are evaluated numerically and show strong agreement with existing numerical results reported in the literature for various diatomic molecular systems. Furthermore, it has been verified that our results are accurate and satisfy both the Heisenberg-Born-Jordan-Dirac commutation relation and the Heisenberg uncertainty principle.
A set of quasi-probability distribution functions which give the correct quantum mechanical marginal distributions of position and momentum is studied. The phase-space distribution does not have to be bilinear in the state function. The Wigner distribution is a special case. A general relationship between the phase-space distribution functions and the rule of associating classical quantities to quantum mechanical operators is derived. This allows the writing of correspondence rules at will,of which the ones presently known are particular cases. The dynamics and other properties of the generalized phase-space distribution are considered.