Article

On the Coulomb singular kernel of Lippmann–Schwinger-type equation

Damir LatypovCyclotron Institute, Texas A&M University, College Station, Texas 77843-3366A. M. MukhamedzhanovInstitute for Nuclear Physics, Tashkent 702132 Uzbekistan

Journal of Mathematical Physicsjournal1992en

ABI

Abstract

A Lippmann–Schwinger-type equation with Coulomb singular kernel is considered. It is shown that all its solutions are singular on the energy shell, k2/2μ=E. In order for this equation to have a solution with a singularity of the type (E−k2/2μ+iε)iα, α is shown to be equal to the Coulomb parameter η. The Coulomb singular kernel in the given class of functions is found to split into a δ function and a kernel which smoothes the singularity.

Topics

Differential Equations and Boundary Problems Differential Equations and Numerical Methods Spectral Theory in Mathematical Physics

Identifiers

DOI: 10.1063/1.529529

Citations and references

Cited by 1 7 references

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