Physical sectors of the confluent hypergeometric functions space

TL;DR

This paper explores the properties of confluent hypergeometric functions using a relaxed factorization approach and investigates their role in solving physical problems, especially in quantum mechanics.

Contribution

It introduces a new perspective on the properties of confluent hypergeometric functions and clarifies their significance in physical solutions, particularly in the Schrödinger equation.

Findings

Properties of confluent hypergeometric functions are linked to physical problem solutions.

Implications for analytical solutions in quantum mechanics are discussed.

The role of these functions in describing physical systems is clarified.

Abstract

A relaxed factorization is used to obtain many of the properties obeyed by the confluent hypergeometric functions. Their implications on the analytical solutions of some interesting physical problems are also studied. It is quite remarkable that, although these properties appear frequently in solving the Schroedinger equation, it has been not clear the role they play in describing the physical systems. The main objective of this communication is precisely to throw some light on the subject.