The one-dimensional Coulomb problem
Abstract
One-dimensional scattering by a Coulomb potential V(x)=\frac {c}{|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, following standard orthogonality relations. The second set consists of anomalous bound states (in a sense to be clarified), which always relax as coherent states.
- Publication:
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Journal of Physics A Mathematical General
- Pub Date:
- July 2009
- DOI:
- 10.1088/1751-8113/42/28/285302
- arXiv:
- arXiv:0905.3978
- Bibcode:
- 2009JPhA...42B5302A
- Keywords:
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- Quantum Physics;
- Condensed Matter - Mesoscale and Nanoscale Physics
- E-Print:
- 29 pages, accepted in J. Phys. A