Coherent States from Combinatorial Sequences

Abstract

We construct coherent states using sequences of combinatorial numbers such as various binomial and trinomial numbers, and Bell and Catalan numbers. We show that these states satisfy the condition of the resolution of unity in a natural way. In each case the positive weight functions are given as solutions of associated Stieltjes or Hausdorff moment problems, where the moments are the combinatorial numbers.

4 pages, Latex; Conference 'Quantum Theory and Symmetries 2', Krakow, Poland, July 2001

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