01-450 Stefan Teufel

A note on the adiabatic theorem without gap condition (17K, Latex 2e) Dec 5, 01

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Abstract. We simplify the proof of the adiabatic theorem of quantum mechanics without gap condition of Avron and Elgart [1] by providing an elementary solution of the ``commutator equation''. In addition, a minor modification of their argument allows for a more direct treatment of eigenvalue crossings. We also obtain simple, explicit conditions that yield information on the rate of convergence in the adiabatic limit.

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