Eigenvalue estimates for Schroedinger operators on metric trees

Details Eigenvalue estimates for Schroedinger operators on metric trees Eigenvalue estimates for Schroedinger operators on metric trees

2007-10-29

arxiv.org/abs/0710.5500v1

Mathematics

Spectral Theory

Scientific paper

10.1016/j.aim.2011.01.001

We consider Schroedinger operators on regular metric trees and prove
Lieb-Thirring and Cwikel-Lieb-Rozenblum inequalities for their negative
eigenvalues. The validity of these inequalities depends on the volume growth of
the tree. We show that the bounds are valid in the endpoint case and reflect
the correct order in the weak or strong coupling limit.

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