A family of (1 + 1)-dimensional harmonic oscillators, subjected to nonlinear potentials, which can generate a quantized energy spectrum
Year: 2026
Type: article
Abstract: We consider a large (perhaps infinite) ensemble of particles. Particle motion is governed by the equation of a harmonic oscillator affected by the addition of a nonlinear potential. The potential has an infinite number of singularities in the position variable, where it is infinite. Consequently, each particle follows oscillatory motion within the potential well confined between two adjacent singularity points. Particle energy depends on the randomly distributed initial conditions of the oscillatory motion. An observer measuring particle energies will obtain an average over the initial conditions. Depending on the nonlinear potential, the measurements may be interpreted as yielding a quantized energy spectrum.
Source: AIP Advances
DOI: 10.1063/5.0344903
Author: Yair Zarmi
Institution: Ben-Gurion University of the Negev
Language: English
Subfield: Statistical and Nonlinear Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: gold
Estimated APC paid: $1,350
OpenAlex ID: W7223300952