Eigenvalue bounds for Schrödinger operators with complex potentials

Abstract

We show that the absolute values of non-positive eigenvalues of Schrödinger operators with complex potentials can be bounded in terms of L_p-norms of the potential. This extends an inequality of Abramov, Aslanyan, and Davies to higher dimensions and proves a conjecture by Laptev and Safronov. Our main ingredient are the uniform Sobolev inequalities of Kenig, Ruiz, and Sogge.

7 pages

References in corpus (2)

• Lieb-Thirring inequalities for Schrödinger operators with complex-valued potentials
• Estimates for eigenvalues of the Schrödinger operator with a complex potential

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