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Durham University

Department of Mathematical Sciences


This week's seminars

Analysis and/of PDE: Improved eigenvalue bounds for Schrödinger operators with slowly decaying potentials

Presented by Jean-Claude Cuenin, Loughborough

14 November 2019 14:00 in CM301

We extend a result of Davies and Nath [1] on the location of eigenvalues of Schrödinger operators $-\Delta+V$ with slowly decaying complex-valued potentials to higher dimensions. We also discuss examples related to the Laptev--Safronov conjecture [2], which stipulates that the absolute value of any complex eigenvalue can be bounded in terms of the $L^q$ norm of $V$, for a certain range of exponents $q$. The talk is based on [3].

[1] Davies, E. B. and Nath, J. Schrödinger operators with slowly decaying potentials J. Comput. Appl. Math., 2002, 148, 1-28

[2] Laptev, A. and Safronov, O. Eigenvalue estimates for Schrödinger operators with complex potentials Comm. Math. Phys., 2009, 292, 29-54

[3] Cuenin, J.-C. Improved eigenvalue bounds for Schr\"odinger operators with slowly decaying potentials arXiv e-prints, 2019, arXiv:1904.03954

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