Meixner- Pollaczek Quantum System

TL;DR

This paper introduces a novel quantum system linked to Meixner-Pollaczek polynomials, expanding the class of solvable quantum models without potential functions, with explicit energy spectrum and wave functions.

Contribution

It presents the first known quantum system associated with Meixner-Pollaczek polynomials, providing explicit solutions and broadening quantum mechanics models.

Findings

New quantum system based on Meixner-Pollaczek polynomials

Explicit energy spectrum and wave functions derived

First such system not previously documented in literature

Abstract

In an effort to achieve our aims (getting larger quantum system) in the recent reformulation of quantum mechanics without potential function [1-5], we obtained a new quantum system associated with Meixner Pollaczek Orthogonal polynomial class (hereby called Meixner - Pollaczek Quantum system). The energy spectrum and wave function of the quantum system were given. To the best of our knowledge, this quantum system is not found in physics literatures.