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The sampling theorem and coherent state systems in quantum mechanics

Arvind, * and Chaturvedi, S and Mukunda, N and Simon, R (2006) The sampling theorem and coherent state systems in quantum mechanics. In: Physica Scripta, 74 . pp. 168-179.

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Abstract

The well-known Poisson Summation Formula is analysed from the perspective of the coherent state systems associated with the Heisenberg–Weyl group. In particular, it is shown that the Poisson Summation Formula may be viewed abstractly as a relation between two sets of bases (Zak bases) arising as simultaneous eigenvectors of two commuting unitary operators in which geometric phase plays a key role. The Zak bases are shown to be interpretable as generalized coherent state systems of the Heisenberg–Weyl group and this, in turn, prompts analysis of the sampling theorem (an important and useful consequence of the Poisson Summation Formula) and its extension from a coherent state point of view leading to interesting results on the properties of von Neumann and finer lattices based on standard and generalized coherent state systems.

Item Type: Journal Article
Additional Information: The copyright belongs to The Royal Swedish Academy of Sciences.
Department/Centre: Division of Physical & Mathematical Sciences > Centre for High Energy Physics
Date Deposited: 06 Sep 2007
Last Modified: 19 Sep 2010 04:39
URI: http://eprints.iisc.ernet.in/id/eprint/11811

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