A method for computing scattering phase shifts and eigenvalues of the Schrödinger equation with singular potentials

1978 ◽  
Vol 19 (6) ◽  
pp. 1426-1432 ◽  
Author(s):  
Friedrich F. Naundorf
Keyword(s):  
Schrödinger Equation ◽  
Schrodinger Equation ◽  
Phase Shifts ◽  
Singular Potentials ◽  
Scattering Phase ◽  
Scattering Phase Shifts

scholarly journals Phase-shifts determination for nucleon–nucleon scattering using velocity-dependent potentials

2016 ◽  
Vol 94 (2) ◽  
pp. 231-235
Author(s):  
M.I. Sayyed
Keyword(s):  
Schrödinger Equation ◽  
Schrodinger Equation ◽  
Yukawa Potential ◽  
Nucleon Nucleon ◽  
Phase Shifts ◽  
S Wave ◽  
Dependent Part ◽  
Dependent Potential ◽  
Scattering Phase ◽  
Square Well

The s-wave time-independent Schrödinger equation with an isotropic velocity-dependent potential is considered. We have used perturbation theory to calculate the scattering phase shifts when the energy is changed by a small amount ΔE from an arbitrary unperturbed value E0. The validity of our results was tested by comparing the perturbed phase shifts to those obtained exactly by solving the Schrödinger equation. We assumed the local potential to have the form of a finite square well and the velocity-dependent part of the potential to have the form of a Yukawa potential.

scholarly journals USING MIXED DATA IN THE INVERSE SCATTERING PROBLEM

2008 ◽  
Vol 22 (23) ◽  
pp. 2181-2189 ◽  
Author(s):  
M. LASSAUT ◽  
S. Y. LARSEN ◽  
S. A. SOFIANOS ◽  
J. C. WALLET
Keyword(s):  
Schrödinger Equation ◽  
Inverse Scattering ◽  
Regular Solution ◽  
Schrodinger Equation ◽  
Scattering Problem ◽  
Inverse Scattering Problem ◽  
Phase Shifts ◽  
Mixed Data ◽  
Monotonic Functions ◽  
Unique Potential

Consider the fixed-ℓ inverse scattering problem. We show that the zeros of the regular solution of the Schrödinger equation, rn(E), which are monotonic functions of the energy, determine a unique potential when the domain of the energy is such that the rn(E) range from zero to infinity. This suggests that the use of the mixed data of phase-shifts {δ(ℓ0, k), k ≥ k0} ∪ {δ(ℓ, k0), ℓ ≥ ℓ0}, for which the zeros of the regular solution are monotonic in both domains, and range from zero to infinity, offers the possibility of determining the potential in a unique way.

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