A new approach for higher-order difference equations and eigenvalue problems via physical potentials

  • Erdal Bas
  • Ramazan OzarslanEmail author
Regular Article


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 \( e_p(t,s)\) . 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.


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© Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Firat University, Science Faculty, Department of MathematicsElazigTurkey

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