Weakly coupled Schroedinger operators on regular metric trees

Abstract

Spectral properties of the Schroedinger operator $A_{\lambda }=-\Delta +\lambda V$ on regular metric trees are studied. It is shown that as $\lambda$ goes to zero the behavior of the negative eigenvalues of $A_{\lambda }$ depends on the global structure of the tree.

References in corpus (2)

• Weakly coupled states on branching graphs
• Schrödinger operator on homogeneous metric trees: spectrum in gaps