Englert, Berthold-Georg; Lee, Kean Loon; Mann, Ady; Revzen, Michael Periodic and discrete Zak bases. (English) Zbl 1092.81021 J. Phys. A, Math. Gen. 39, No. 7, 1669-1682 (2006). 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. Reviewer: Jan Hamhalter (Praha) Cited in 2 Documents 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) Keywords:Zak basis; position and momentum operator PDFBibTeX XMLCite \textit{B.-G. Englert} et al., J. Phys. A, Math. Gen. 39, No. 7, 1669--1682 (2006; Zbl 1092.81021) Full Text: DOI arXiv