The one-dimensional Coulomb Problem

Details The one-dimensional Coulomb Problem The one-dimensional Coulomb Problem

2009-05-25

arxiv.org/abs/0905.3978v1

G Abramovici et al 2009 J. Phys. A: Math. Theor. 42 285302 (29pp)

Physics

Quantum Physics

29 pages, accepted in J. Phys. A

Scientific paper

10.1088/1751-8113/42/28/285302

One-dimensional scattering by a Coulomb potential V(x)=lambda/|x| 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, respecting standard orthogonality relations. The second set consists of "anomalous"} bound states (in a sense to be clarified), which always relax as coherent states.

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