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We study a correct statement of the scattering problem arising for quantumcharged scalar particles on the Reissner-Nordstr\"{o}m black holes when takinginto account the own electric field of black hole. The elements of thecorresponding S-matrix are explored in the form convenient to physicalapplications and for applying numerical methods. Some further possible issuesare outlined.Comment: 12 pages, LaTeX with using the ijmpd1.sty file from the package of  World Scientific Publishing Co., to appear in Int. J. Mod. Phys. D7 (1998

CORRECT STATEMENT OF A SCATTERING PROBLEM FOR QUANTUM CHARGED SCALAR PARTICLES ON THE REISSNER–NORDSTRÖM BLACK HOLES