Spectrum of the hydrogen atom in Snyder space in a semiclassical approximation

TL;DR

This paper investigates how Snyder space modifies the hydrogen atom spectrum using a semiclassical approach, revealing first-order corrections for s-states and second-order for others due to phase space topology differences.

Contribution

It introduces a semiclassical method to analyze the hydrogen spectrum in Snyder space, highlighting the order of corrections based on angular momentum states.

Findings

First-order spectrum corrections for l=0 states.

Second-order corrections for l≠0 states.

Topology of phase space influences correction order.

Abstract

We study the spectrum of the hydrogen atom in Snyder space in a semiclassical approximation based on a generalization of the Born-Sommerfeld quantization rule. While the corrections to the standard quantum mechanical spectrum arise at first order in the Snyder parameter for the $l=0$ states, they are of second order for $l\neq 0$. This can be understood as due to the different topology of the regions of integration in phase space.