Almost complete coherent state subsystems and partial reconstruction of wavefunctions in the Fock-Bargmann phase-number representation

作者：Calixto M^*; Guerrero J; Sanchez Monreal J C

来源：Journal of Physics A-Mathematical and Theoretical, 2012, 45(24): 244029.

DOI：10.1088/1751-8113/45/24/244029

We provide (partial) reconstruction formulas and discrete Fourier transforms for wavefunctions in standard Fock-Bargmann (holomorphic) phase-number representation from a finite number N of phase samples {0(k) = 2 pi k/N}(K=0)(N-1) for a given mean number p of particles. The resulting coherent state subsystem S = {vertical bar z(k) = p(1/2)e(i theta k)} is complete (a frame) for truncated Hilbert spaces (finite number of particles) and reconstruction formulas are exact. For an unbounded number of particles, S is %26apos;almost complete%26apos; (a pseudo-frame) and partial reconstruction formulas are provided along with a study of the accuracy of the approximation, which tends to be exact when p %26lt; N and/or N -%26gt; infinity. %26lt;br%26gt;This article is part of a special issue of Journal of Physics A: Mathematical and Theoretical devoted to %26apos;Coherent states: mathematical and physical aspects%26apos;.

• 出版日期2012-6-22