Bound states in a nonlinear Kronig-Penney model

TL;DR

This paper investigates bound states in a nonlinear Kronig-Penney model, revealing high degeneracy of the ground state and near-degeneracy of the highest bound state under specific conditions, applicable to simple periodic potentials.

Contribution

It introduces analysis of bound states in a nonlinear Kronig-Penney potential, highlighting degeneracy phenomena not previously detailed.

Findings

Ground state can be highly degenerate

High-energy bound states can have similar energies to the ground state

Degeneracy occurs under specific conditions in periodic potentials

Abstract

We study the bound states of a Kronig Penney potential for a nonlinear one-dimensional Schroedinger equation. This potential consists of a large, but not necessarily infinite, number of equidistant delta-function wells. We show that the ground state can be highly degenerate. Under certain conditions furthermore, even the bound state that would normally be the highest can have almost the same energy as the ground state. This holds for simple periodic potentials as well.