Estimations for negative spectral bands of three‐dimensional periodical Schrödinger operator

1993 ◽  
Vol 34 (3) ◽  
pp. 936-942 ◽  
Author(s):  
G. V. Galloonov ◽  
V. L. Oleinik ◽  
B. S. Pavlov
Keyword(s):  
Schrödinger Operator ◽  
Three Dimensional ◽  
Schrodinger Operator ◽  
Spectral Bands

Resonances for Slowly Varying Perturbations of a Periodic Schrödinger Operator

2002 ◽  
Vol 54 (5) ◽  
pp. 998-1037 ◽  
Author(s):  
Mouez Dimassi
Keyword(s):  
Schrödinger Operator ◽  
Positive Constant ◽  
Asymptotic Expansions ◽  
Periodic Potential ◽  
Schrodinger Operator ◽  
Small Positive Constant ◽  
Spectral Bands ◽  
Periodic Schrödinger Operator ◽  
Shape Resonances

AbstractWe study the resonances of the operator . Here V is a periodic potential, φ a decreasing perturbation and h a small positive constant. We prove the existence of shape resonances near the edges of the spectral bands of , and we give its asymptotic expansions in powers of .

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.

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