Linear nonlocal problem for the abstract time-dependent non-homogeneous Schr\'odinger equation

Autor:	Sytnyk, Dmytro, Melnik, Roderick
Rok vydání:	2016
Předmět:	Mathematical Physics Mathematics - Dynamical Systems Mathematics - Functional Analysis Quantum Physics
Druh dokumentu:	Working Paper
Popis:	A nonlocal-in-time problem for the abstract Schr\"odinger equation is considered. By exploiting the linear nature of nonlocal condition we derive an exact representation of the solution operator under assumptions that the spectrum of Hamiltonian is contained in the horizontal strip of complex plane. The derived representation permits us to establish the necessary and sufficient conditions for the problem's well-posedness and the existence of its mild, strong solutions. Furthermore, we present new sufficient conditions for the existence of solution which extend the available results to the case when some nonlocal parameters are unbounded. Two examples are provided. Comment: 19 pages, 2 examples, 2 figures
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/1609.08670 Zobrazit plný text záznamu View this record from Arxiv