Completeness of Coherent States Associated with Self-Similar Potentials and Ramanujan's Integral Extension of the Beta Function

TL;DR

This paper explores the relationship between coherent states for self-similar potentials and Ramanujan's integral extension of the beta function, providing a new integral decomposition of identity.

Contribution

It introduces a novel integral decomposition of coherent states linked to self-similar potentials and connects it with Ramanujan's extension of the beta function.

Findings

Derived a complex integral decomposition of identity for coherent states.

Established a connection between coherent states and Ramanujan's integral extension.

Highlights the mathematical relationship between quantum states and special functions.

Abstract

A decomposition of identity is given as a complex integral over the coherent states associated with a class of shape-invariant self-similar potentials. There is a remarkable connection between these coherent states and Ramanujan's integral extension of the beta function.