Exponential Perturbative Expansions and Coordinate Transformations
| Autor: | Fernando Casas, Ana Arnal, Cristina Chiralt |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2020 |
| Předmět: |
Unitarity
Floquet–Magnus expansion Applied Mathematics lcsh:T57-57.97 lcsh:Mathematics Linear system coordinate transformations General Engineering Magnus expansion lcsh:QA1-939 lcsh:QA75.5-76.95 Schrödinger equation Exponential function Computational Mathematics symbols.namesake Ordinary differential equation lcsh:Applied mathematics. Quantitative methods symbols Applied mathematics Perturbation theory (quantum mechanics) lcsh:Electronic computers. Computer science Quantum Mathematics |
| Zdroj: | Mathematical and Computational Applications, Vol 25, Iss 50, p 50 (2020) Mathematical and Computational Applications Volume 25 Issue 3 Repositori Universitat Jaume I Universitat Jaume I |
| ISSN: | 2297-8747 |
| Popis: | 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&ndash Magnus expansion for periodic systems, the quantum averaging technique, and the Lie&ndash 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 Schrö dinger equation. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
|