The sampling theorem and coherent state systems in quantum mechanics

DOI10.1088/0031-8949/74/2/004zbMATH Open1117.81077arXivquant-ph/0601059OpenAlexW2162881039MaRDI QIDQ5485582

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Publication date: 30 August 2006

Published in: (Search for Journal in Brave)

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 generalised 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 properties of von Neumann and finer lattices based on standard and generalised coherent state systems.

Full work available at URL: https://arxiv.org/abs/quant-ph/0601059

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