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Adiabatic theorem and spectral concentration

I. Arbitrary order spectral concentration for the stark effect in atomic physics

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Abstract

The spectral concentration of arbitrary order for the Stark effect is proved to exist for a large class of Hamiltonians appearing in nonrelativistic and relativistic quantum mechanics. The results are consequences of an abstract result about the spectral concentration for self-adjoint operators. A general form of the adiabatic theorem of quantum mechanics, generalizing an earlier result of the author as well as some results by Lenard, is also proved.

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Author notes

  1. G. Nenciu

    Present address: Central Institute of Physics, PO Box Mg.6, Bucharest, Romania

Authors and Affiliations

  1. Laboratory of Theoretical Physics, Joint Institute for Nuclear Research, SU-141980, Dubna, USSR

    G. Nenciu

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  1. G. Nenciu
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Communicated by B. Simon

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Nenciu, G. Adiabatic theorem and spectral concentration. Commun.Math. Phys. 82, 121–135 (1981). https://doi.org/10.1007/BF01206948

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  • DOI: https://doi.org/10.1007/BF01206948

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