A new class of coherent states with Meixner-Pollaczek polynomials for the Gol'dman-Krivchenkov Hamiltonian

TL;DR

This paper introduces a novel class of coherent states based on Meixner-Pollaczek polynomials tailored for the Gol'dman-Krivchenkov Hamiltonian, expanding the mathematical framework of quantum state representations.

Contribution

It constructs generalized coherent states using Meixner-Pollaczek polynomials with a new identity resolution, specific to the Gol'dman-Krivchenkov Hamiltonian.

Findings

New coherent states with Meixner-Pollaczek polynomials are explicitly constructed.

The states satisfy a novel identity resolution within the Hamiltonian's Hilbert space.

The approach broadens the class of coherent states applicable to quantum systems.

Abstract

A class of generalized coherent states with a new type of the identity resolution are constructed by replacing the labeling parameter zn/n! of the canonical coherent states by Meixner-Pollaczek polynomials with specific parameters. The constructed coherent states belong to the state Hilbert space of the Gol'dman-Krivchenkov Hamiltonian.