Straight Quantum Waveguide with Robin Boundary Conditions

TL;DR

This paper studies the spectral properties of a quantum particle in a straight waveguide with Robin boundary conditions, identifying conditions for bound states and analyzing eigenvalues numerically.

Contribution

It introduces a variable Robin boundary condition model, localizes the essential spectrum, and provides numerical analysis of eigenvalues and eigenfunctions.

Findings

Essential spectrum is localized under certain conditions.

Bound states exist when specific criteria are met.

Eigenvalues and eigenfunctions are characterized numerically.

Abstract

We investigate spectral properties of a quantum particle confined to an infinite straight planar strip by imposing Robin boundary conditions with variable coupling. Assuming that the coupling function tends to a constant at infinity, we localize the essential spectrum and derive a sufficient condition which guarantees the existence of bound states. Further properties of the associated eigenvalues and eigenfunctions are studied numerically by the mode-matching technique.