Open Access Research

Solutions of the Schrödinger equation in a Hilbert space

Alexander Boichuk* and Oleksander Pokutnyi

Author Affiliations

Laboratory of boundary value problems of the theory of differential equations, Institute of Mathematics of NAS of Ukraine, Tereshenkivska, 3, Kiev, 01601, Ukraine

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Boundary Value Problems 2014, 2014:4  doi:10.1186/1687-2770-2014-4


Dedicated to the academician Kiguradze I.T.

Published: 6 January 2014

Abstract

Necessary and sufficient conditions for the existence of a solution of a boundary-value problem for the Schrödinger equation are obtained in the linear and nonlinear cases. Analytic solutions are represented using the generalized Green operator.

Keywords:
normally resolvable operator; generalized Green operator; Schrödinger equation