Relativistic Stationary Schrodinger Equation for Many Particle System and Its Applications

TL;DR

This paper introduces a relativistic modification to the stationary Schrödinger equation for many-particle systems, considering space-time inversion symmetry, with potential applications in fields like quarkonium modeling.

Contribution

It proposes a new relativistic form of the stationary Schrödinger equation based on space-time inversion symmetry for many-particle systems.

Findings

Eigenvalues differ from traditional models due to relativistic effects.

Application potential in quarkonium and other particle systems.

Discussion of symmetry implications in quantum systems.

Abstract

Basing on the fundamental symmetry that the space-time inversion is equivalent to particle-antiparticle transformation, a relativistic modification on the stationary Schrodinger equation for many-particle system is made. The eigenvalue in the center of mass system is no longer equal to the negative of binding energy simply. The possible applications in various fields (e.g. the model of quarkonium) are discussed.