The gaps in the spectrum of the Schrödinger operator
Volume 69 / 2005
Banach Center Publications 69 (2005), 91-102
MSC: Primary
35P15; Secondary 58G25.
DOI: 10.4064/bc69-0-5
Abstract
We obtain inequalities between the eigenvalues of the Schrödinger operator on a compact domain $\Omega$ of a submanifold $M$ in $R^{N}$ with boundary $\partial \Omega$, which generalize many existing inequalities for the Laplacian on a bounded domain of a Euclidean space. We also establish similar inequalities for a closed minimal submanifold in the unit sphere, which generalize and improve Yang-Yau's result.
