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Author  |
Blanes, S.; Casas, F.; Oteo, J.A.; Ros, J. |
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Title |
A pedagogical approach to the Magnus expansion |
Type |
Journal Article |
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Year |
2010 |
Publication |
European Journal of Physics |
Abbreviated Journal |
Eur. J. Phys. |
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Volume |
31 |
Issue |
4 |
Pages |
907-918 |
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Keywords |
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Abstract |
Time-dependent perturbation theory as a tool to compute approximate solutions of the Schrodinger equation does not preserve unitarity. Here we present, in a simple way, how the Magnus expansion (also known as exponential perturbation theory) provides such unitary approximate solutions. The purpose is to illustrate the importance and consequences of such a property. We suggest that the Magnus expansion may be introduced to students in advanced courses of quantum mechanics. |
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Address |
[Blanes, S.] Univ Politecn Valencia, Inst Matemat Multidisciplinar, E-46022 Valencia, Spain, Email: serblaza@imm.upv.es |
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Publisher |
Iop Publishing Ltd |
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Language |
English |
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Series Title |
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Series Volume |
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Series Issue |
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Edition |
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ISSN |
0143-0807 |
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Notes |
ISI:000279393800024 |
Approved |
no |
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Is ISI |
yes |
International Collaboration |
no |
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Call Number |
IFIC @ pastor @ |
Serial |
259 |
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Author |
Casas, F.; Oteo, J.A.; Ros, J. |
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Title |
Unitary transformations depending on a small parameter |
Type |
Journal Article |
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Year |
2012 |
Publication |
Proceedings of the Royal Society A |
Abbreviated Journal |
Proc. R. Soc. A |
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Volume |
468 |
Issue |
2139 |
Pages |
685-700 |
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Keywords |
perturbation theory; quantum mechanics; unitary transformation; Magnus expansion |
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Abstract |
We formulate a unitary perturbation theory for quantum mechanics inspired by the Lie-Deprit formulation of canonical transformations. The original Hamiltonian is converted into a solvable one by a transformation obtained through a Magnus expansion. This ensures unitarity at every order in a small parameter. A comparison with the standard perturbation theory is provided. We work out the scheme up to order ten with some simple examples. |
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Address |
[Oteo, J. A.; Ros, J.] Univ Valencia, Dept Fis Teor, E-46100 Valencia, Spain, Email: rosj@uv.es |
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Thesis |
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Publisher |
Royal Soc |
Place of Publication |
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Editor |
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Language |
English |
Summary Language |
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Original Title |
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Series Editor |
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Abbreviated Series Title |
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Series Volume |
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Edition |
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ISSN |
1364-5021 |
ISBN |
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Notes |
WOS:000300185400005 |
Approved |
no |
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Is ISI |
yes |
International Collaboration |
no |
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Call Number |
IFIC @ pastor @ |
Serial |
893 |
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