WKB-method for the 1D Schrödinger equation in the semi-classical limit: enhanced phase treatment
| Autor: | Bernhard Ujvari, Anton Arnold, Christian Klein |
|---|---|
| Přispěvatelé: | Institut für Analysis und Scientific Computing, Vienna University of Technology (TU Wien), Institut de Mathématiques de Bourgogne [Dijon] (IMB), Centre National de la Recherche Scientifique (CNRS)-Université de Franche-Comté (UFC), Université Bourgogne Franche-Comté [COMUE] (UBFC)-Université Bourgogne Franche-Comté [COMUE] (UBFC)-Université de Bourgogne (UB), Austrian Science Fund (FWF)bi-national FWFI3538-N32Clear Sky VenturesFrench National Research Agency (ANR)isite BFC project NAANoDANR-17-EURE-0002 EIPHIEuropean Union Horizon 2020 research and innovation program under the Marie Sklodowska-Curie RISE 2017 Grant778010, ANR-17-EURE-0002,EIPHI,Ingénierie et Innovation par les sciences physiques, les savoir-faire technologiques et l'interdisciplinarité(2017) |
| Jazyk: | angličtina |
| Rok vydání: | 2021 |
| Předmět: |
Computer Networks and Communications
Computation Phase (waves) Semiclassical physics Schrödinger equation 010103 numerical & computational mathematics 01 natural sciences Classical limit WKB approximation symbols.namesake Higher order WKB-approximation Applied mathematics [INFO]Computer Science [cs] Limit (mathematics) 0101 mathematics [MATH]Mathematics [math] Physics Uniformly accurate scheme Applied Mathematics 010101 applied mathematics Computational Mathematics Spectral methods Highly oscillating wave functions Asymptotically correct finite difference scheme symbols Spectral method Software |
| Zdroj: | BIT Numerical Mathematics BIT Numerical Mathematics, Springer Verlag, 2021, ⟨10.1007/s10543-021-00868-x⟩ |
| ISSN: | 0006-3835 1572-9125 |
| DOI: | 10.1007/s10543-021-00868-x⟩ |
| Popis: | International audience; This paper is concerned with the efficient numerical computation of solutions to the 1D stationary Schrödinger equation in the semiclassical limit in the highly oscillatory regime. A previous approach to this problem based on explicitly incorporating the leading terms of the WKB approximation is enhanced in two ways: first a refined error analysis for the method is presented for a not explicitly known WKB phase, and secondly the phase and its derivatives will be computed with spectral methods. The efficiency of the approach is illustrated for several examples. |
| Databáze: | OpenAIRE |
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