On completeness of coherent states in noncommutative spaces with generalised uncertainty principle

TL;DR

This paper investigates the completeness of coherent states in noncommutative spaces under a generalized uncertainty principle, deriving the resolution of identity using analytic solutions to moment problems.

Contribution

It provides explicit conditions and methods for establishing the resolution of unity for coherent states in noncommutative quantum models with generalized uncertainty relations.

Findings

Derived positive definite weight functions for coherent states

Solved the Stieltjes and Hausdorff moment problems analytically

Established completeness criteria for noncommutative space models

Abstract

Coherent states are required to form a complete set of vectors in the Hilbert space by providing the resolution of identity. We study the completeness of coherent states for two different models in a noncommutative space associated with the generalised uncertainty relation by finding the resolution of unity with a positive definite weight function. The weight function, which is sometimes known as the Borel measure, is obtained through explicit analytic solutions of the Stieltjes and Hausdorff moment problem with the help of the standard techniques of inverse Mellin transform.