Exponential perturbative expansions and coordinate transformations
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866929220398088192 |
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| author | Arnal, Ana Casas, Fernando Chiralt, Cristina |
| author_facet | Arnal, Ana Casas, Fernando Chiralt, Cristina |
| contents | 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 can be formulated for any time-dependent linear system of ordinary differential equations. All the procedures (except the standard perturbation theory) lead to approximate solutions preserving by construction unitarity when applied to the time-dependent Schrödinger equation. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_12955 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Exponential perturbative expansions and coordinate transformations Arnal, Ana Casas, Fernando Chiralt, Cristina Numerical Analysis 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 can be formulated for any time-dependent linear system of ordinary differential equations. All the procedures (except the standard perturbation theory) lead to approximate solutions preserving by construction unitarity when applied to the time-dependent Schrödinger equation. |
| title | Exponential perturbative expansions and coordinate transformations |
| topic | Numerical Analysis |
| url | https://arxiv.org/abs/2401.12955 |