Conformal Mapping of Relativistic Quantum Bound Systems to Eliminate Potential Fields

TL;DR

This paper extends a conformal mapping technique that removes potential terms from quantum equations, demonstrating its applicability to relativistic Klein-Gordon systems, thus broadening the method's scope in quantum physics.

Contribution

It introduces the application of an isometric conformal transformation to Klein-Gordon equations, expanding the method's utility to relativistic quantum bound systems.

Findings

Transformation successfully eliminates potential terms in Klein-Gordon equations

Method previously applied to Schrödinger equation now extended to relativistic case

Potential for simplifying relativistic quantum calculations

Abstract

In two recent papers, an isometric conformal transformation has been introduced that eliminates potential interaction terms from the Schr\"odinger equation for central potential problems. The method has been demonstrated for both the hydrogen atom and three-dimensional harmonic oscillator. Here, it is shown that the same transformation technique can also be applied to central potential problems formulated using the Klein-Gordon equation.