Integral Representations for the Solutions of the Generalized Schroedinger Equation in a Finite Interval  

作　　者：Anar Adiloglu Nabiev Rauf Kh. Amirov 

机构地区：[1]Department of Mathematics, Cumhuriyet University, Sivas, Turkey

出　　处：《Advances in Pure Mathematics》2015年第13期777-795,共19页理论数学进展（英文）

摘　　要：We reduce the initial value problem for the generalized Schroedinger equation with piecewise-constant leading coefficient to the system of Volterra type integral equations and construct new useful integral representations for the fundamental solutions of the Schroedinger equation. We also investigate some significant properties of the kernels of these integral representations. The integral representations of fundamental solutions enable to obtain the basic integral equations, which are a powerful tool for solving inverse spectral problems.We reduce the initial value problem for the generalized Schroedinger equation with piecewise-constant leading coefficient to the system of Volterra type integral equations and construct new useful integral representations for the fundamental solutions of the Schroedinger equation. We also investigate some significant properties of the kernels of these integral representations. The integral representations of fundamental solutions enable to obtain the basic integral equations, which are a powerful tool for solving inverse spectral problems.

关 键 词：One Dimensional SCHROEDINGER EQUATION Fundamental SOLUTIONS Transformation Operator Inte-gral Representation Differential EQUATION with Discontinues Coefficient Kernel of an INTEGRAL Op-erator INTEGRAL EQUATION Method of Successive APPROXIMATIONS 

分 类 号：O1[理学—数学]