Linear nonlocal problem for the abstract time-dependent non-homogeneous Schrödinger equation

Abstract

A nonlocal-in-time problem for the abstract Schrödinger 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.

19 pages, 2 examples, 2 figures

References in corpus (4)

• Floquet-Magnus Theory and Generic Transient Dynamics in Periodically Driven Many-Body Quantum Systems
• Many-Body Quantum Electrodynamics Networks: Non-Equilibrium Condensed Matter Physics with Light
• Comparison and unification of non-Hermitian and Lindblad approaches with applications to open quantum optical systems
• Tunable Chern insulator with shaken optical lattices

Cited by in corpus (3)

• Parallel numerical method for nonlocal-in-time Schrödinger equation
• On recovering of solutions of Schrödinger equations from their time averages
• Regularity of complexified hyperbolic equations with integral conditions