高阶差分方程和本征值问题的物理势解法
A New Approach for Higher Order Difference Equations and Eigenvalue problems via Physical Potentials
摘要：
本文利用δ指数函数，从不同的角度给出了N阶常系数非齐次线性常差分方程的参数变分法.这种新方法的优点是使我们能够研究封闭形式的差分方程的解。该方法还得到了三个差分本征值问题的支持，即二阶Sturm-Liouville问题（也称为一维薛定谔方程，具有库仑势）、氢原子方程和四阶弛豫差分方程.利用变参数法，通过δ指数函数和δ三角函数，求出了含库仑势的二阶Sturm-Liouville问题和氢原子方程解的和表示，以及四阶离散弛豫问题的解析解.
英文摘要：
In this study, we give the variation of parameters method from a different viewpoint for the Nth order inhomogeneous linear ordinary difference equations with constant coefficient by means of delta exponential function . Advantage of this new approachment is to enable us to investigate the solution of difference equations in the closed form. Also, the method is supported with three difference eigenvalue problems, the second-order Sturm-Liouville problem, which is called also one dimensional Schrödinger equation, having Coulomb potential, hydrogen atom equation, and the fourth-order relaxation difference equations. We find sum representation of solution for the second order discrete Sturm-Liouville problem having Coulomb potential, hydrogen atom equation, and 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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