Upper bound on the multiplicity of eigenvalues of the Sch\"odinger-Dirichlet operator in dimension two

TL;DR

This paper provides an upper bound on the maximum number of eigenvalues that can coincide for the Schrödinger-Dirichlet operator in two dimensions, using a proof based on a generalized Morse Lemma.

Contribution

It introduces a new upper bound for eigenvalue multiplicities in 2D Schrödinger-Dirichlet operators utilizing a generalized Morse Lemma approach.

Findings

Established an explicit upper bound on eigenvalue multiplicities in 2D

Applied a generalized Morse Lemma for the proof

Contributed to spectral theory of differential operators

Abstract

We establish an upper bound on the multiplicity of eigenvalues of the Sch\"odinger-Dirichlet operator in dimension two. We give a proof based on a generalized Morse Lemma due to Cheng \cite{Ch}.