Abstract
The paper deals with asymptotic expansions in cylindrical coordinates for the Schrödinger equation of the diamagnetic Coulomb problem with infinite nuclear mass. The basis functions introduced by Liu and Starace are analysed: analytical asymptotic expansions are given for the basis functions and eigenvalues belonging to them. Using these, analytical asymptotic expansions are obtained for the coupling coefficients and solutions of the system of second-order ordinary differential equations which arise if the wavefunction is expanded in terms of the Liu - Starace basis functions. The role of the asymptotic expansions is elucidated for the numerical solution of the non-adiabatic approximation and for finding non-trivial auto-ionizing states.
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More From: Journal of Physics A: Mathematical and General
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