A symbolic-numerical method for solving the differential equation describing the states of polarizable particle in Coulomb potential
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Methods for solving the differential equation describing the wave functions of a polarizable particle in the Coulomb potential are discussed. Relations between the coefficients under which the general solution of this equation can be found in analytical form are obtained. For the case of zero polarizability, the general 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 computer-aided analysis using numerical and analytical methods and visualization of the resulting solutions.
KeywordsGeneral Solution Kepler Problem Coulomb Field Functional Object Heun Equation
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