Factorization method for Schrodinger equation in relativistic configuration space and q-deformations
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Date
2013
Authors
Journal Title
Journal ISSN
Volume Title
Publisher
Maik Nauka/Interperiodica/Springer
Access Rights
info:eu-repo/semantics/closedAccess
Abstract
Review paper is devoted to the relativistic configuration space (RCS) concept, a version of the relativistic Quantum Mechanics in RCS, the generalization of the Dirac-Infeld-Hall factorization method in the framework of the noncommutative differential calculus natural for RCS, different versions of the deformed oscillators, emerging as the generalization of the harmonic oscillator for RCS. In the formulation of the Newton-Wigner postulates for the relativistic localized states the hypothesis of commutativity of the position operator components is silently accepted as an evident fact. In the present work it is shown that commutativity is not necessary condition and the alternative (noncommutative) approach to the relativistic position operator and localization concept can be realized in a framework of the physically as well as mathematically comprehensive scheme. The different generalizations of the Dirac-Infeld-Hall factorization method for this case are constructed. This method enables us to find out all possible generalizations of the most important nonrelativistic integrable case-the harmonic oscillator. It is shown also that the relativistic oscillator = q-oscillator.
Description
Keywords
Quantum, Localizability, Oscillators
Journal or Series
Physics of Particles and Nuclei
WoS Q Value
Q4
Scopus Q Value
Q3
Volume
44
Issue
3
