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International Journal of Theoretical Physics

, Volume 53, Issue 5, pp 1628–1636 | Cite as

Analysis of Adiabatic Approximation Using Stable Hamiltonian Method

  • Yi-Tian Ding
Article

Abstract

In this paper, we deal with the adiabatic approximation of general Hamiltonians by splitting it into two parts, with one part a Hamiltonian that has at least one time-independent eigenstate up to a phase factor. We first develop the method of finding this kind of Hamiltonians. Then the relationship between adiabatic approximation and these Hamiltonians is discussed. Applying this to a general case, we give both a necessary condition and a sufficient condition for adiabatic approximation, followed by a spin-half example to illustrate.

Keywords

Adiabatic approximation Stable Hamiltonian Necessary condition Sufficient condition 

Notes

Acknowledgements

The work was supported by Basic Sciences Training Funds of China NO. J1103212.

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Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  1. 1.Department of PhysicsShandong UniversityJinanChina

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