Bound states in straight quantum waveguides with combined boundary conditions

TL;DR

This paper studies the discrete energy levels of a quantum particle in a straight waveguide with mixed boundary conditions, providing theoretical results and numerical examples of eigenvalues and eigenfunctions.

Contribution

It offers new insights into the spectral properties of quantum waveguides with combined boundary conditions, including existence and absence results for discrete spectra.

Findings

Proven conditions for the existence of discrete spectrum

Proven conditions for the absence of discrete spectrum

Numerical computation of eigenfunctions and eigenvalues

Abstract

We investigate the discrete spectrum of the Hamiltonian describing a quantum particle living in the two-dimensional straight strip. We impose the combined Dirichlet and Neumann boundary conditions on different parts of the boundary. Several statements on the existence or the absence of the discrete spectrum are proven for two models with combined boundary conditions. Examples of eigenfunctions and eigenvalues are computed numerically.