Analytic structure and power series expansion of the Jost function for the two-dimensional problem
2012 (English)In: Journal of Physics A: Mathematical and Theoretical, ISSN 1751-8113, Vol. 45, no 13, 135209- p.Article in journal (Refereed) Published
For a two-dimensional quantum-mechanical problem, we obtain a generalized power series expansion of the S-matrix that can be done near an arbitrary point on the Riemann surface of the energy, similar to the standard effective-range expansion. In order to do this, we consider the Jost function and analytically factorize its momentum dependence that causes the Jost function to be a multi-valued function. The remaining single-valued function of the energy is then expanded in the power series near an arbitrary point in the complex energy plane. A systematic and accurate procedure has been developed for calculating the expansion coefficients. This makes it possible to obtain a semi-analytic expression for the Jost function (and therefore for the S-matrix) near an arbitrary point on the Riemann surface and use it, for example, to locate the spectral points (bound and resonant states) as the S-matrix poles. The method is applied to a model similar to those used in the theory of quantum dots.
Place, publisher, year, edition, pages
2012. Vol. 45, no 13, 135209- p.
IdentifiersURN: urn:nbn:se:su:diva-76044DOI: 10.1088/1751-8113/45/13/135209ISI: 000302133400011OAI: oai:DiVA.org:su-76044DiVA: diva2:525797
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