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A Symbolic–Numerical Method for Solving the Differential Equation Describing the States of Polarizable Particle in Coulomb Potential

V. M. Red’kov
Organization: Stepanov Institute of Physics, National Academy of Sciences of Belarus
A. V. Chichurin
Organization: John Paul II Catholic University of Lublin
Journal / Anthology

Programming and Computer Software
Year: 2014
Volume: 40
Issue: 2
Page range: 86–92

Methods for solving the differential equation describing the wave functions of a polarizable parti cle in the Coulomb potential are discussed. Relations between the coefficients under which the general solu tion of this equation can be found in analytical form are obtained. For the case of zero polarizability, the gen eral solution to this equation in terms of special functions is obtained; for the first values of the parameter j, plots of the corresponding solutions are presented. For nonzero polarizability and certain specially chosen values of the energy level parameter, solutions possessing the required physical properties for the varying parameter j are constructed on fairly large intervals of the argument values using numerical methods and functional objects of the type DifferentialRoot. Instructions in Mathematica are presented that allow com puteraided analysis using numerical and analytical methods and visualization of the resulting solutions.

*Mathematica Technology > Programming

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