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Schrödinger operators with magnetic fields

III. Atoms in homogeneous magnetic field

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Abstract

We prove a large number of results about atoms in constant magnetic field including (i) Asymptotic formula for the ground state energy of Hydrogen in large field, (ii) Proof that the ground state of Hydrogen in an arbitrary constant field hasL z = 0 and of the monotonicity of the binding energy as a function ofB, (iii) Borel summability of Zeeman series in arbitrary atoms, (iv) Dilation analyticity for arbitrary atoms with infinite nuclear mass, and (v) Proof that every once negatively charged ion has infinitely many bound states in non-zero magnetic field with estimates of the binding energy for smallB and largeL z .

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Authors and Affiliations

  1. Department of Physics, Princeton University, 08544, Princeton, NJ, USA

    J. E. Avron

  2. Department of Mathematics, University of Viginia, 22903, Charlottesville, VA, USA

    I. W. Herbst

  3. Department of Mathematics and Physics, Princeton University, 08544, Princeton, NJ, USA

    B. Simon

Authors
  1. J. E. Avron
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  2. I. W. Herbst
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  3. B. Simon
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Additional information

Communicated by J. Ginibre

On leave at Department of Mathematics, California Institute of Technology, Pasadena, CA 91125 for 1980/81

Supported by USNSF Grant MCS-78-00101

Supported by USNSF Grant MCS-78-01885; on leave at Department of Mathematics, California Institute of Technology, Pasadena, CA 91125 for 1980/81

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Avron, J.E., Herbst, I.W. & Simon, B. Schrödinger operators with magnetic fields. Commun. Math. Phys. 79, 529–572 (1981). https://doi.org/10.1007/BF01209311

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  • DOI: https://doi.org/10.1007/BF01209311

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