FAST TRACK COMMUNICATION: Transmission reflection problem with a potential of the form of the derivative of the delta function
Abstract
Regarding the quantum mechanical transmission-reflection problem in one dimension with a potential of the form of the derivative of the Dirac delta function δ'(x) = dδ(x)/dx, Christiansen et al recently found that, depending on how δ'(x) is interpreted, there can be a resonance which leads to partial transmission. This is in contrast to the earlier consensus that such a potential allows no transmission. The δ'(x) can be regarded as the narrow-width limit of a certain function Δ'(x) of a finite range. Christiansen et al assumed a rectangular function for Δ'(x). We examine various other forms and how the resonance depends on the shape of Δ'(x). We also present some general observations related to the 'threshold anomaly'.
- Publication:
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Journal of Physics A Mathematical General
- Pub Date:
- July 2007
- DOI:
- Bibcode:
- 2007JPhA...40..685T