Rakityansky, Sergei AnatoljevichElander, N.2012-05-172012-05-172012-03Rakityansky, 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. 1-29.1751-8113 (print)1751-8121 (online)10.1088/1751-8113/45/13/135209http://hdl.handle.net/2263/18756For 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© 2012 IOP Publishing LtdJost functionTransformation of the radial equationComplex rotationExplicit separation of the non-analytic factorsAnalytic structure of the Jost functionsTwo-dimensional quantum-mechanical problemEffective range (Nuclear physics)Quantum dots (QDs)Postprint Article