Numerical results a quantum waveguide with Mixed boundary conditions

TL;DR

This paper numerically investigates the eigenvalues of a quantum Hamiltonian in a 3D waveguide with mixed boundary conditions, electric field, and a disc window, revealing how these factors influence quantum states.

Contribution

It provides a numerical analysis of eigenvalue existence for a quantum waveguide with mixed boundary conditions and external electric field, a novel combination in this context.

Findings

Eigenvalues are affected by the electric field strength.

Boundary conditions significantly influence eigenvalue existence.

The disc window size impacts the spectral properties.

Abstract

This article is devoted to the numerical study of the existence of the eigenvalues of the Hamiltonian describing a quantum particle living on three dimensional straight strip of width $d$ in the presence of an electric field of constant intensity $F$ in the direction perpendicular to the electron plane. We impose Neumann boundary conditions on a disc window of radius $a$ and Dirichlet boundary conditions on the remaining part of the boundary of the strip.