On the eigenvalue asymptotics of Zonal Schrödinger operators in even metric and non-even metric

Nonclassical Eigenvalue Asymptotics for Operators of Schrödinger

which depends on the volume u)n of the unit sphere in R n and the beta function. Assuming /3 < 2 we see that integral (2) becomes divergent if V (x) vanishes to a sufficiently high order. The simplest such potential is V(x,y) = \x\\y\P o n R n + R m . The Weyl (volume counting) principle, when applied to the corresponding Schrödinger operator — A-hV(x), fails to predict discrete spectrum below ...

Eigenvalue Asymptotics of the Even-Dimensional Exterior Landau-Neumann Hamiltonian

Weakly Coupled Schrödinger Operators on Regular Metric Trees

Spectral properties of the Schrödinger operator Aλ = −∆+λV on regular metric trees are studied. It is shown that as λ goes to zero the behavior of the negative eigenvalues of Aλ depends on the global structure of the tree. Mathematics Subject Classification: 34L40, 34B24, 34B45.

Eigenvalue Estimates for Schrödinger Operators on Metric Trees

We consider Schrödinger operators on regular metric trees and prove LiebThirring 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.

on the effect of linear & non-linear texts on students comprehension and recalling

چکیده ندارد.