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 $l\ne 0$. This can be understood as due to the different topology of the regions of integration in phase space.

7 pages

References in corpus (3)

• Hydrogen-atom spectrum under a minimal-length hypothesis
• Hydrogen atom in momentum space with a minimal length
• Quantum mechanics on a curved Snyder space

Cited by in corpus (11)

• Quantum field theory in generalised Snyder spaces
• Bumblebee gravity and particle motion in Snyder noncommutative spacetime structures
• Lorentzian Snyder spacetimes and their Galilei and Carroll limits from projective geometry
• Snyder-type spaces, twisted Poincaré algebra and addition of momenta
• Particle on a Torus Knot: Constrained Dynamics and Semi-Classical Quantization in a Magnetic Field
• Particle on a torus knot: Symplectic analysis
• Classical electrodynamics on Snyder space
• $\kappa$-Galilean and $\kappa$-Carrollian noncommutative spaces of worldlines
• Two-particle system in Coulomb potential for twist-deformed space-time
• Twist deformations of Newtonian Schwarzschild-(Anti-)de Sitter classical system
• Some features of a Schwarzchild Black Hole from a Snyder perspective