Hypergeometric Connotations of Quantum Equations

TL;DR

This paper demonstrates that fundamental quantum equations like Schrödinger and Klein-Gordon can be derived from hypergeometric differential equations, including their nonlinear variants, revealing a new mathematical foundation for quantum physics.

Contribution

It introduces a novel approach by deriving key quantum equations from hypergeometric differential equations, unifying linear and nonlinear cases.

Findings

Quantum equations are derivable from hypergeometric equations

Nonlinear quantum equations also follow from hypergeometric forms

Provides a new mathematical perspective on quantum mechanics

Abstract

We show that the Schr\"odinger and Klein-Gordon equations can both be derived from an Hypergeometric differential equation. The same applies to non linear generalizations of these equations.