Analytic structure and power series expansion of the Jost function for the two-dimensional problem

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dc.contributor.author Rakityansky, Sergei Anatoljevich
dc.contributor.author Elander, N.
dc.date.accessioned 2012-05-17T06:14:14Z
dc.date.available 2012-05-17T06:14:14Z
dc.date.issued 2012-03
dc.description.abstract 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 multivalued 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. en
dc.description.librarian nf2012 en
dc.description.uri http://www.iop.org/EJ/journal/JPhysA en_US
dc.identifier.citation Rakityansky, SA & Elander, N 2012, 'Analytic structure and power series expansion of the Jost function for the two-dimensional problem', Journal of Physics A: Mathematical and Theoretical, vol. 45, no. 13, art. no. 135209, pp. 1-29. en
dc.identifier.issn 1751-8113 (print)
dc.identifier.issn 1751-8121 (online)
dc.identifier.other 10.1088/1751-8113/45/13/135209
dc.identifier.uri http://hdl.handle.net/2263/18756
dc.language.iso en en_US
dc.publisher Institute of Physics en_US
dc.rights © 2012 IOP Publishing Ltd en_US
dc.subject Jost function en
dc.subject Transformation of the radial equation en
dc.subject Complex rotation en
dc.subject Explicit separation of the non-analytic factors en
dc.subject Analytic structure of the Jost functions en
dc.subject Two-dimensional quantum-mechanical problem en
dc.subject.lcsh Effective range (Nuclear physics) en
dc.subject.lcsh Quantum dots (QDs) en
dc.title Analytic structure and power series expansion of the Jost function for the two-dimensional problem en
dc.type Postprint Article en


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