A MOURRE ESTIMATE FOR A SCHRÖDINGER OPERATOR ON A BINARY TREE

2000 ◽  
Vol 12 (12) ◽  
pp. 1655-1667 ◽  
Author(s):  
C. ALLARD ◽  
R. FROESE
Keyword(s):  
Schrödinger Operator ◽  
Binary Tree ◽  
Invariant Subspaces ◽  
Schrodinger Operator ◽  
Conjugate Operator ◽  
Order Difference ◽  
First Order ◽  
Decay Condition ◽  
Mourre Estimate

Let G be a binary tree with vertices V and H be a Schrödinger operator acting on ℓ2 (V). A decomposition of the space ℓ2 (V) into invariant subspaces is exhibited yielding a conjugate operator A for use in the Mourre estimate. We show that for potentials q satisfying a first order difference decay condition, a Mourre estimate for H holds.

Inverse scattering for the higher order Schrödinger operator with a first order perturbation

2019 ◽  
Vol 27 (3) ◽  
pp. 409-427
Author(s):  
Hua Huang ◽  
Zhiwen Duan ◽  
Quan Zheng
Keyword(s):  
Inverse Scattering ◽  
Schrödinger Operator ◽  
Scattering Matrix ◽  
Higher Order ◽  
Zero Order ◽  
Schrodinger Operator ◽  
Scattering Problems ◽  
First Order ◽  
Fixed Energy ◽  
First Order Perturbation

Abstract This paper concerns inverse scattering problems at a fixed energy for the higher order Schrödinger operator with the first order perturbed potentials in dimensions {n\geq 3} . We show that the scattering matrix uniquely determines the first order perturbed potentials and the zero order potentials.

scholarly journals Bound states of a system of two bosons with a spherically potential on a lattice

2021 ◽  
Vol 2070 (1) ◽  
pp. 012023
Author(s):  
J.I. Abdullaev ◽  
Sh.H. Ergashova ◽  
Y.S. Shotemirov
Keyword(s):  
Invariant Subspace ◽  
Schrödinger Operator ◽  
Bound States ◽  
Three Dimensional ◽  
Invariant Subspaces ◽  
Bound State ◽  
Schrodinger Operator ◽  
Dimensional Lattice

Abstract We consider a Hamiltonian of a system of two bosons on a three-dimensional lattice Z 3 with a spherically simmetric potential. The corresponding Schrödinger operator H(k) this system has four invariant subspaces L(123), L(1), L(2) and L(3). The Hamiltonian of this system has a unique bound state over each invariant subspace L(1), L(2) and L(3). The corresponding energy values of these bound states are calculated exactly.

scholarly journals On the two-dimensional Schrödinger operator with an attractive potential of the Bessel-Macdonald type

2020 ◽  
pp. 168385
Author(s):  
Wellisson B. De Lima ◽  
Oswaldo M. Del Cima ◽  
Daniel H.T. Franco ◽  
Bruno C. Neves
Keyword(s):  
Schrödinger Operator ◽  
Attractive Potential ◽  
Two Dimensional ◽  
Schrodinger Operator
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