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

Rauf Kh.  Amirov; Anar Adiloglu  Nabiev

doi:10.4236/apm.2015.513072

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APM Vol.5 No.13 , November 2015

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

Anar Adiloglu Nabiev^*, Rauf Kh. Amirov

Abstract: 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.

Keywords: 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

Cite this paper: Nabiev, A. and Amirov, R. (2015) Integral Representations for the Solutions of the Generalized Schroedinger Equation in a Finite Interval. Advances in Pure Mathematics, 5, 777-795. doi: 10.4236/apm.2015.513072.

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