Schrödinger operator. Estimates for number of bound states as function-theoretical problem

1992 ◽  
pp. 1-54 ◽  
Author(s):  
M. S. Birman ◽  
M. Z. Solomyak
Keyword(s):  
Schrödinger Operator ◽  
Bound States ◽  
Theoretical Problem ◽  
Schrodinger Operator

scholarly journals Bound states of the Schrödinger operator of a system of three bosons on a lattice

2016 ◽  
Vol 188 (1) ◽  
pp. 994-1005
Author(s):  
S. N. Lakaev ◽  
A. R. Khalmukhamedov ◽  
A. M. Khalkhuzhaev
Keyword(s):  
Schrödinger Operator ◽  
Bound States ◽  
Schrodinger Operator

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.

The Agmon spectral function for molecular hamiltonians with symmetry restrictions

1993 ◽  
Vol 440 (1910) ◽  
pp. 621-638 ◽  
Keyword(s):  
Quantum Mechanics ◽  
Spectral Function ◽  
Schrödinger Operator ◽  
Spectral Properties ◽  
Bound States ◽  
Schrödinger Operators ◽  
Schrodinger Operators ◽  
Schrodinger Operator ◽  
Polyatomic Systems

In this paper we introduce symmetry considerations into our earlier work, which was concerned with geometric spectral properties of Schrödinger operators including the N -body operators of quantum mechanics. The point of emphasis is a function introduced by Shmuel Agmon which we have named the Agmon spectral function. We show that this function is symmetric for an N -body Schrödinger operator restricted to a subspace of prescribed symmetry. We then show how it can be used to obtain criteria for the finiteness and infiniteness of bound states of polyatomic systems.

INTRINSIC RESONANT TUNNELING PROPERTIES OF THE ONE-DIMENSIONAL SCHRÖDINGER OPERATOR WITH A DELTA DERIVATIVE POTENTIAL

2013 ◽  
Vol 28 (01) ◽  
pp. 1350203 ◽  
Author(s):  
A. V. ZOLOTARYUK ◽  
Y. ZOLOTARYUK
Keyword(s):  
Schrödinger Operator ◽  
Resonant Tunneling ◽  
Bound States ◽  
Delta Function ◽  
Schrodinger Operator ◽  
Range Limit ◽  
One Dimensional ◽  
The One ◽  
Adjoint Operators ◽  
Delta Derivative

Restricting ourselves to a simple rectangular approximation but using properly a two-scale regularization procedure, additional resonant tunneling properties of the one-dimensional Schrödinger operator with a delta derivative potential are established, which appear to be lost in the zero-range limit. These "intrinsic" properties are complementary to the main already proved result that different regularizations of Dirac's delta function produce different limiting self-adjoint operators. In particular, for a given regularizing sequence, a one-parameter family of connection condition matrices describing bound states is constructed. It is proposed to consider the convergence of transfer matrices when the potential strength constant is involved into the regularization process, resulting in an extension of resonance sets for the transmission across a δ′-barrier.

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