On the Schrödinger Equation for Time-Dependent Hamiltonians with a Constant Form Domain

Balmaseda Martín, Ángel Aitor; Lonigro, Davide; Pérez Pardo, Juan Manuel

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On the Schrödinger Equation for Time-Dependent Hamiltonians with a Constant Form Domain

Author(s): Balmaseda Martín, Ángel Aitor; Lonigro, Davide; Pérez Pardo, Juan Manuel

Publisher: MDPI AG

Issued date: 2022-01-11

Citation: Balmaseda, A., Lonigro, D., & Pérez-Pardo, J. M. (2022). On the Schrödinger Equation for Time-Dependent Hamiltonians with a Constant Form Domain. In Mathematics, 10(2), 218-238

ISSN: 2227-7390

DOI: https://doi.org/10.3390/math10020218

xmlui.dri2xhtml.METS-1.0.item-contributor-funder: Comunidad de Madrid
Ministerio de Ciencia, Innovación y Universidades (España)
Universidad Carlos III de Madrid

Sponsor: A.B. and J.M.P.-P. acknowledge support provided by the “Ministerio de Ciencia e Innovación” Research Project PID2020-117477GB-I00, by the QUITEMAD Project P2018/TCS-4342 funded by Madrid Government (Comunidad de Madrid-Spain) and by the Madrid Government (Comunidad de Madrid-Spain) under the Multiannual Agreement with UC3M in the line of “Research Funds for Beatriz Galindo Fellowships” (C&QIG-BG-CM-UC3M), and in the context of the V PRICIT (Regional Programme of Research and Technological Innovation). A.B. acknowledges financial support by “Universidad Carlos III de Madrid” through Ph.D. Program Grant PIPF UC3M 01-1819 and through its mobility grant in 2020. D.L. was partially supported by “Istituto Nazionale di Fisica Nucleare” (INFN) through the project “QUANTUM” and the Italian National Group of Mathematical Physics (GNFM-INdAM).

Project: Gobierno de España. PID2020-117477GB-I00
Comunidad de Madrid. P2018/TCS-4342
Universidad Carlos III de Madrid. C&QIG-BG-CM-UC3M
Universidad Carlos III de Madrid. UC3M 01-1819

Keywords: Schrödinger equation , Time-dependent hamiltonian , Hilbert scales , Time-dependent domain

URI: http://hdl.handle.net/10016/35247

Rights: © 2022 by the authors. Licensee MDPI, Basel, Switzerland.
Atribución 3.0 España

Abstract:

We study two seminal approaches, developed by B. Simon and J. Kisynski, to the wellposedness 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 dom [+]

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