Examples of Plentiful Discrete Spectra in0 Infinite Spatial Cruciform Quantum Waveguides

TL;DR

This paper constructs specific spatial cruciform quantum waveguides demonstrating that their discrete spectra can have arbitrarily large multiplicities, advancing understanding of spectral properties in quantum waveguide models.

Contribution

It introduces a method to design cruciform waveguides with unbounded discrete spectrum multiplicities, a novel result in quantum spectral theory.

Findings

Discrete spectrum multiplicity can be made arbitrarily large.

Construction of waveguides with prescribed spectral properties.

Advancement in understanding spectral multiplicities in quantum waveguides.

Abstract

Spatial cruciform quantum waveguides (the Dirichlet problem for Laplace operator) are constructed such that the total multiplicity of the discrete spectrum exceeds any preassigned number.