7. Lakhdar Gaffour, Effects of nonstationary space-time geometry on observables

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Volume 22: Pages 288-292, 2009

Effects of nonstationary space-time geometry on observables

Lakhdar Gaffour 1

1Department of Physics, University of Sidi-Bel-Abbes, Algeria and LSIIT ENSP, Strasbourg, France

In a previous paper, fundamental equations of quantum mechanics have been established in time-varying domain. It turns out that these equations are the generalization of those of usual quantum mechanics established in stationary space-time. This present work attempts to draw consequences and effects of the nonstationary space-time domain on observables by analyzing these equations. The main theoretical findings from this analysis can be summed as follows: A pseudocovariance of equations is observed. It can be seen that the functional wave function associated to the particle possesses a dynamical modal nature; each mode has an instantaneous wave number. Moreover, observables are subjected to space-time effects. As an illustration, we give an example corresponding to a linear motion increasing or decreasing the domain.

Keywords: Quantum Mechanics, Schrödinger, Klein–Gordon and Dirac Equations, Observables, Time-Varying Domain, Wave Function, Covariance, Real Nondegenerate Transformations of a Variable Domain, Conformal Mapping, Relativity, Einstein’s Relation of Energy, Mass at the Rest

Received: February 10, 2009; Accepted: May 2, 2009; Published Online: July 14, 2009