Periodic solutions of Schrodinger equation in Hilbert space
A. A. Boichuk, A. A. Pokutnyi
TL;DR
This paper establishes conditions for the existence of solutions to the Schrödinger equation in Hilbert spaces and provides explicit periodic solutions using generalized Green's operators.
Contribution
It introduces necessary and sufficient conditions for boundary value problems of the Schrödinger equation and constructs explicit periodic solutions in Hilbert spaces.
Findings
Conditions for existence of solutions are derived.
Explicit periodic solutions are constructed using generalized Green's operators.
Results apply to both linear and nonlinear Schrödinger equations.
Abstract
Necessary and sufficient conditions for existence of boundary value problem of Schrodinger equation are obtained in linear and nonlinear cases. Periodic analytical solutions are represented using generalized Green's operator
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Taxonomy
TopicsNumerical methods for differential equations · Matrix Theory and Algorithms · Advanced Mathematical Modeling in Engineering