The one-dimensional coulomb problem

G. Abramovici, Y. Avishai

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14 Scopus citations

Abstract

One-dimensional scattering by a Coulomb potential is studied for both repulsive (c > 0) and attractive (c < 0) cases. Two methods of regularizing the singularity at x = 0 are used, yielding the same conclusion, namely, that the transmission vanishes. For an attractive potential (c < 0), two groups of bound states are found. The first one consists of regular (Rydberg) bound states, following standard orthogonality relations. The second set consists of anomalous bound states (in a sense to be clarified), which always relax as coherent states.

Original languageEnglish
Article number285302
JournalJournal of Physics A: Mathematical and Theoretical
Volume42
Issue number28
DOIs
StatePublished - 19 Nov 2009
Externally publishedYes

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