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Localization in deformed quantum mechanics

Simón Codriansky

Published Jan 1, 1995• 0 citations
OpenAlex

Abstract

In this talk it is shown that in one version of q-algebras there exists states-a subset of the coherent states- that have negligible dispersion in energy, position and momentum.

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Abstract We develop a deformation quantization approach to quantum mechanics that exhibits a nonzero minimal uncertainty in position through the modification of commutation relations for the operators of position and momentum. Deformation quantization is a method of quantizing a classical Hamiltonian system by suitably deforming the Poisson algebra of the system. The developed theory of deformation quantization is non-formal. An appropriate integral formula for the star-product is introduced, along with a suitable space of functions on which the star-product is well defined. A C*-algebra of observables and a space of states are constructed. Moreover, an operator representation in momentum space is presented. Finally, an example of states of maximal localization is given in terms of generalized Wigner functions.