Weighted Eigenvalue Problem Approach To The Critical Value Determination Of Screened Coulomb Potential Systems

Abstract

In this work, the radial time-independent Schrödinger equation of a screened Coulomb potential system at the zero energy limit is first converted to a weighted eigenvalue problem of an ordinary differential operator. Then, by using an appropriate coordinate transformation, the differential equation is transformed into a form whose first and second order derivative related terms become same as the Extended Jacobi Polynomials' differential equation's corresponding terms. Only difference is the appearance of a multiplicative operator which can be considered as an effective potential. Work focuses on the point whether the solution is obtained easily depending on the structure of this potential. In this direction a screened Coulomb potential with a specific rational screening function is considered. The analytical solutions for the critical values of the screening parameter and the form of the wave function at the threshold of the continous spectrum are obtained. (© 2004 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)