RT Journal Article
T1 On the Schrödinger Equation for Time-Dependent Hamiltonians with a Constant Form Domain
A1 Balmaseda Martín, Ángel Aitor
A1 Lonigro, Davide
A1 Pérez Pardo, Juan Manuel
AB We study two seminal approaches, developed by B. Simon and J. Kisynski, to the wellposednessof the Schrödinger equation with a time-dependent Hamiltonian. In both cases, theHamiltonian is assumed to be semibounded from below and to have a constant form domain, but apossibly non-constant operator domain. The problem is addressed in the abstract setting, withoutassuming any specific functional expression for the Hamiltonian. The connection between the twoapproaches is the relation between sesquilinear forms and the bounded linear operators representingthem. We provide a characterisation of the continuity and differentiability properties of form-valuedand operator-valued functions, which enables an extensive comparison between the two approachesand their technical assumptions.
PB MDPI AG
SN 2227-7390
YR 2022
FD 2022-01-11
LK https://hdl.handle.net/10016/35247
UL https://hdl.handle.net/10016/35247
LA eng
NO 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 fundedby Madrid Government (Comunidad de Madrid-Spain) and by the Madrid Government (Comunidadde Madrid-Spain) under the Multiannual Agreement with UC3M in the line of “Research Funds forBeatriz Galindo Fellowships” (C&QIG-BG-CM-UC3M), and in the context of the V PRICIT (RegionalProgramme 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 throughits 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).
DS e-Archivo
RD 27 jul. 2024