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Commutators and self-adjointness of Hamiltonian operators

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Abstract

A time dependent approach to self-adjointness is presented and it is applied to quantum mechanical Hamiltonians which are not semi-bounded. Sufficient conditions are given for self-adjointness of Schrödinger and Dirac Hamiltonians with potentials which are unbounded at infinity. The method is the introduction of an auxiliary operatorN≧0 whose rate of change (commutator with the Hamiltonian) is bounded by a multiple ofN.

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Authors and Affiliations

  1. Advanced Studies Center, Battelle Institute, Carouge-Geneva, Switzerland

    William G. Faris

  2. Mathematics Department, University of Rochester, Rochester, N.Y., USA

    Richard B. Lavine

Authors
  1. William G. Faris
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  2. Richard B. Lavine
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Faris, W.G., Lavine, R.B. Commutators and self-adjointness of Hamiltonian operators. Commun.Math. Phys. 35, 39–48 (1974). https://doi.org/10.1007/BF01646453

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  • DOI: https://doi.org/10.1007/BF01646453

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