A new approach for higher-order difference equations and eigenvalue problems via physical potentials
Firat University, Science Faculty, Department of Mathematics, 23119, Elazig, Turkey
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Accepted: 19 February 2019
Published online: 6 June 2019
In the present paper the variation of parameters method for the N -th-order non-homogeneous linear ordinary difference equations with constant coefficient is introduced by means of the delta exponential function . Thanks to this new advantageous approach, one can investigate the solution of higher-order difference equations which can be considered important for many mathematical models. Moreover, we bring forth the method with three difference eigenvalue problems involving the second-order Sturm-Liouville problem, called one-dimensional Schrödinger equation, with Coulomb potential, hydrogen atom equation and the fourth-order relaxation difference equation. Sum representations of the solutions of the second-order discrete Sturm-Liouville problem having Coulomb potential and hydrogen atom equation are found out. In addition, we get analytical solution of the fourth-order discrete relaxation problem by the variation of parameters method via delta exponential and delta trigonometric functions.
© Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature, 2019