scholarly journals Inverse scattering problem for quarkonium systems. I. One-dimensional formalism and methodology. [bound state, algebraic technique]

1977 ◽  
Author(s):  
H.B. Thacker ◽  
C. Quigg ◽  
J.L. Rosner
Keyword(s):  
Inverse Scattering ◽  
Scattering Problem ◽  
Inverse Scattering Problem ◽  
Bound State ◽  
One Dimensional ◽  
Algebraic Technique

The direct and inverse problem in Newtonian scattering

1991 ◽  
Vol 118 (1-2) ◽  
pp. 119-131 ◽  
Author(s):  
M. A. Astaburuaga ◽  
Claudio Fernández ◽  
Víctor H. Cortés
Keyword(s):  
Inverse Problem ◽  
Phase Space ◽  
Inverse Scattering ◽  
Scattering Problem ◽  
Inverse Scattering Problem ◽  
Dimensional Case ◽  
Classical Particle ◽  
Scattering Operator ◽  
One Dimensional ◽  
The One

SynopsisIn this paper we study the direct and inverse scattering problem on the phase space for a classical particle moving under the influence of a conservative force. We provide a formula for the scattering operator in the one-dimensional case and we settle the properties of the potential that can be deduced from it. We also study the question of recovering the shape of the barriers which can be seen from −∞ and ∞. An example is given showing that these barriers are not uniquely determined by the scattering operator.

scholarly journals Random Schrödinger operators with a background potential

2019 ◽  
Vol 27 (4) ◽  
pp. 253-259
Author(s):  
Hayk Asatryan ◽  
Werner Kirsch
Keyword(s):  
Inverse Scattering ◽  
Density Of States ◽  
Anderson Localization ◽  
Scattering Problem ◽  
Schrödinger Operators ◽  
Inverse Scattering Problem ◽  
Random Schrödinger Operators ◽  
Integrated Density Of States ◽  
Schrodinger Operators ◽  
One Dimensional

Abstract We consider one-dimensional random Schrödinger operators with a background potential, arising in the inverse scattering problem. We study the influence of the background potential on the essential spectrum of the random Schrödinger operator and obtain Anderson localization for a larger class of one-dimensional Schrödinger operators. Further, we prove the existence of the integrated density of states and give a formula for it.

NONLOCAL SEPARABLE SOLUTIONS OF THE INVERSE SCATTERING PROBLEM

1993 ◽  
Vol 08 (18) ◽  
pp. 3163-3184 ◽  
Author(s):  
TONY GHERGHETTA ◽  
YOICHIRO NAMBU
Keyword(s):  
Inverse Scattering ◽  
Scattering Problem ◽  
Inverse Scattering Problem ◽  
Bound State ◽  
Separable Potential ◽  
Nonlocal Potential ◽  
S Wave ◽  
Weakly Bound ◽  
Square Well ◽  
Nonlocal Separable Potential

We extend the nonlocal separable potential solutions of Gourdin and Martin for the inverse scattering problem to the case where sin δ0 has more than N zeroes, δ0 being the s-wave scattering phase shift and δ0(0) − δ0(∞) = Nπ. As an example we construct the solution for the particular case of 4 He and show how to incorporate a weakly bound state. Using a local square well potential chosen to mimic the real 4 He potential, we compare the off-shell extension of the nonlocal potential solution with the exactly solvable square well. We then discuss how a nonlocal potential might be used to simplify the many-body problem of liquid 4 He .

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