# On negative eigenvalues of low-dimensional Schr\"{o}dinger operators

@article{Molchanov2011OnNE, title={On negative eigenvalues of low-dimensional Schr\"\{o\}dinger operators}, author={Stanislav Molchanov and Boris Vainberg}, journal={arXiv: Mathematical Physics}, year={2011} }

The paper concerns upper and lower estimates for the number of negative eigenvalues of one- and two-dimensional Schr\"{o}dinger operators and more general operators with the spectral dimensions $d\leq 2$. The classical Cwikel-Lieb-Rosenblum (CLR) upper estimates require the corresponding Markov process to be transient, and therefore the dimension to be greater than two. We obtain CLR estimates in low dimensions by transforming the underlying recurrent process into a transient one using partial…

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