98-370 J.E. Avron and A. Elgart

The Adiabatic Theorem of Quantum Mechanics (30K, LATeX 2e) May 26, 98

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Abstract. We prove the adiabatic theorem for quantum evolution without the traditional gap condition. We show that the theorem holds essentially in all cases where it can be formulated. In particular, our result implies that the adiabatic theorem holds also for eigenvalues embedded in the continuous spectrum. If there is information on the H\"older continuity of the spectral measure, then one can also estimate the rate at which the adiabatic limit is approached.

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