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arXiv:hep-th/0404044 · Progress of Theoretical Physics

Generalized Heisenberg Dynamics

Yoshiharu Kawamura A

Published Aug 1, 2004• 1 citation
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Abstract

We formulate a dynamical system based on many-index objects. These objects yield a generalization of the Heisenberg equation. Systems describing harmonic oscillators are presented.
DOI
10.1143/ptp.112.299

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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.