Eigenvalue bounds in one dimensional Schrodinger's equation with ultra-short potentials

TL;DR

This paper derives bounds on energy spectra and particle probabilities in one-dimensional Schrödinger's equation with ultra-short potentials, providing insights relevant for nanodevice confinement.

Contribution

It introduces a general solution to Schrödinger's equation for ultra-short potentials and establishes bounds on energy and probability spectra.

Findings

Energy spectra have definite bounds for ultra-short potentials.

Particle probability distributions are bounded in these potentials.

Results are applicable to nanodevice particle confinement.

Abstract

The problem of a particle localized in a ultra-short potential in one dimension is considered. By proposing a general solution to Schrodinger;s equation we show that the energy spectra and the probability of the particle have definite bounds for an arbitrary ultra-short potential. These results are relevant for the confinement of particles in nanodevices.