APM  Vol.5 No.13 , November 2015
Integral Representations for the Solutions of the Generalized Schroedinger Equation in a Finite Interval
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.

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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