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On an inhomogeneous Schrödinger equation and its solutions in scattering theory

van Haeringen, H., 1979, In : Journal of Mathematical Physics. 20, 5, p. 861-867 7 p.

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  • H van Haeringen
We prove that ψs,l, the partial‐wave projection of the irregular Coulomb wavefunction ψs, is a solution of an inhomogeneous Schrödinger equation. New expressions for ψs,l and ψs are obtained in terms of the Coulomb Green functions GC,l and GC, respectively. We discuss irregular solutions, the analogs of ψs, for Coulomb‐like and short‐range potentials. We find that in general these functions do not approach asymptotically the scattering amplitude times an outgoing spherical wave, in contrast to the pure Coulomb function ψs.
Original languageEnglish
Pages (from-to)861-867
Number of pages7
JournalJournal of Mathematical Physics
Volume20
Issue number5
Publication statusPublished - 1979

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