On the Schrödinger Equation for Time-Dependent Hamiltonians with a Constant Form Domain
Balmaseda A, Lonigro D, Pérez-Pardo JM (2022)
Publication Type: Journal article
Publication year: 2022
Journal
Book Volume: 10
Article Number: 218
Journal Issue: 2
DOI: 10.3390/math10020218
Abstract
We study two seminal approaches, developed by B. Simon and J. Kisyński, to the well-posedness of the Schrödinger equation with a time-dependent Hamiltonian. In both cases, the Hamiltonian is assumed to be semibounded from below and to have a constant form domain, but a possibly non-constant operator domain. The problem is addressed in the abstract setting, without assuming any specific functional expression for the Hamiltonian. The connection between the two approaches is the relation between sesquilinear forms and the bounded linear operators representing them. We provide a characterisation of the continuity and differentiability properties of form-valued and operator-valued functions, which enables an extensive comparison between the two approaches and their technical assumptions.
Authors with CRIS profile
Involved external institutions
Universidad Carlos III de Madrid (UC3M)
Spain (ES)
University of Bari Aldo Moro / Università degli Studi di Bari Aldo Moro
Italy (IT)
Spain (ES)
University of Bari Aldo Moro / Università degli Studi di Bari Aldo Moro
Italy (IT)
How to cite
APA:
Balmaseda, A., Lonigro, D., & Pérez-Pardo, J.M. (2022). On the Schrödinger Equation for Time-Dependent Hamiltonians with a Constant Form Domain. Mathematics, 10(2). https://dx.doi.org/10.3390/math10020218
MLA:
Balmaseda, Aitor, Davide Lonigro, and Juan Manuel Pérez-Pardo. "On the Schrödinger Equation for Time-Dependent Hamiltonians with a Constant Form Domain." Mathematics 10.2 (2022).
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