Coherent States for Generalized Laguerre Functions

TL;DR

This paper constructs a Hamiltonian with eigenfunctions as generalized Laguerre functions, develops related coherent states using the Gazeau-Klauder approach, and compares them with other known methods, revealing similarities to P"oschl-Teller potential states.

Contribution

It introduces explicit Hamiltonian and coherent state constructions for generalized Laguerre functions, expanding the understanding of their quantum state representations.

Findings

Coherent states exhibit properties similar to P"oschl-Teller potential states.

Resolution of unity and overlap properties are successfully analyzed.

Comparisons with Barut-Girardello and Klauder-Perelomov methods are provided.

Abstract

We explicitly construct a Hamiltonian whose exact eigenfunctions are the generalized Laguerre functions. Moreover, we present the related raising and lowering operators. We investigate the corresponding coherent states by adopting the Gazeau-Klauder approach, where resolution of unity and overlapping properties are examined. Coherent states are found to be similar to those found for a particle trapped in a P\"oschl-Teller potential of the trigonometric type. Some comparisons with Barut-Girardello and Klauder-Perelomov methods are noticed.