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The one-dimensional Coulomb Problem
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.Comment: 29 pages, accepted in J. Phys.
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