1-D Harmonic Oscillator in Snyder Space, the Classic and the Quantum

TL;DR

This paper explores the classical and quantum behaviors of a 1-D harmonic oscillator in Snyder space, revealing an effective cutoff and modified energy spectra through an equivalent oscillator model.

Contribution

It introduces a novel analysis of the harmonic oscillator in Snyder space, deriving an effective model with altered parameters and spectra.

Findings

Classical trajectories exhibit an effective cutoff to high frequencies.

Quantum analysis yields an equivalent harmonic oscillator with modified mass and frequency.

Modified energy spectra differ from the standard harmonic oscillator.

Abstract

The 1-D dimension harmonic oscillator in Snyder space is investigated in its classical and quantum versions. The classical trajectory is obtained and the semiclassical quantization from the phase space trajectories is discussed. In the meanwhile, an effective cutoff to high frequencies is found. The quantum version is developed and an equivalent usual harmonic oscillator is obtained through an effective mass and an effective frequency introduced in the model. This modified parameters give us an also modified energy spectra.