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Periodic and discrete Zak bases. (English) Zbl 1092.81021

The Zak transform is considered as a mapping of the Hilbert space on a line to Hilbert space on a torus. Periodic and discrete Zak bases which are unbiased are studied. The position and momentum operators are given as differential operators in the Zak representation. A possible application of the Zak bases to quantum information theory is discussed.

MSC:

81Q70 Differential geometric methods, including holonomy, Berry and Hannay phases, Aharonov-Bohm effect, etc. in quantum theory
81S05 Commutation relations and statistics as related to quantum mechanics (general)
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