p-Adic and Adelic Free Relativistic Particle

TL;DR

This paper explores p-adic and adelic quantum mechanics for a free relativistic particle, revealing eigenfunctions and discrete spacetime structures at the Planck scale within the adelic framework.

Contribution

It introduces p-adic and adelic eigenfunctions for a relativistic particle and demonstrates the existence of discrete spacetime structures at the Planck scale.

Findings

Existence of p-adic and adelic eigenfunctions.

Discrete spacetime structure at the Planck scale.

Adelic approach reveals novel quantum states.

Abstract

We consider spectral problem for a free relativistic particle in p-adic and adelic quantum mechanics. In particular, we found p-adic and adelic eigenfunctions. Within adelic approach there exist quantum states that exhibit discrete structure of spacetime at the Planck scale.