An Isaac Newton Institute Workshop

Spectral Theory and its Applications

Some eigenvalue inequalities for Schrödinger operators with positive potentials.

Author: A. Laptev (Royal Institute of Technology, Sweden)


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.