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# STP

## Seminar

### Some eigenvalue inequalities for Schr\"{o}dinger operators with positive potentials

Laptev, A (Royal Institute of Technology, Sweden)
Friday 28 July 2006, 14:00-14:50

Seminar Room 1, Newton Institute

#### Abstract

We shall discuss some estimates from below on the ratio of the $\lambda_k/\lambda_1$ where $\lambda_k$ are the eigenvalues of the Dirichlet boundary value problem for the operator $-\Delta +V$, $V\ge 0$, in $L^2(\Omega)$, $\Omega\subset{\Bbb R}^d$. Surprisingly some of such estimates are independent of $V$ or $\Omega$. This is my joint paper with R.Frank and S.Molchanov.

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