DOI: 10.1063/5.0344903 ISSN: 2158-3226
A family of (1 + 1)-dimensional harmonic oscillators, subjected to nonlinear potentials, which can generate a quantized energy spectrum
Yair ZarmiWe 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.