TY - JOUR

T1 - The one-dimensional coulomb problem

AU - Abramovici, G.

AU - Avishai, Y.

PY - 2009/11/19

Y1 - 2009/11/19

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=70449497351&partnerID=8YFLogxK

U2 - 10.1088/1751-8113/42/28/285302

DO - 10.1088/1751-8113/42/28/285302

M3 - Article

AN - SCOPUS:70449497351

VL - 42

JO - Journal of Physics A: Mathematical and Theoretical

JF - Journal of Physics A: Mathematical and Theoretical

SN - 1751-8113

IS - 28

M1 - 285302

ER -