Exponential Perturbative Expansions and Coordinate Transformations
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Título
Exponential Perturbative Expansions and Coordinate TransformationsFecha de publicación
2020Editor
MDPIISSN
1300-686X; 2297-8747Cita bibliográfica
Arnal, A.; Casas, F.; Chiralt, C. Exponential Perturbative Expansions and Coordinate Transformations. Math. Comput. Appl. 2020, 25, 50.Tipo de documento
info:eu-repo/semantics/articleVersión de la editorial
https://www.mdpi.com/2297-8747/25/3/50Versión
info:eu-repo/semantics/publishedVersionPalabras clave / Materias
Resumen
We propose a unified approach for different exponential perturbation techniques used in
the treatment of time-dependent quantum mechanical problems, namely the Magnus expansion,
the Floquet–Magnus expansion for ... [+]
We propose a unified approach for different exponential perturbation techniques used in
the treatment of time-dependent quantum mechanical problems, namely the Magnus expansion,
the Floquet–Magnus expansion for periodic systems, the quantum averaging technique, and the
Lie–Deprit perturbative algorithms. Even the standard perturbation theory fits in this framework.
The approach is based on carrying out an appropriate change of coordinates (or picture) in each case,
and it can be formulated for any time-dependent linear system of ordinary differential equations.
All of the procedures (except the standard perturbation theory) lead to approximate solutions
preserving by construction unitarity when applied to the time-dependent Schrödinger equation. [-]
Publicado en
Math. Comput. Appl. 2020, 25, 50.Proyecto de investigación
MTM2016-77660-P (AEI/FEDER, UE), UJI-B2019-17 and GACUJI/2020/05Derechos de acceso
info:eu-repo/semantics/openAccess
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