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

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.