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Eigenvalue Bounds for Perturbations of Schrödinger Operators and Jacobi Matrices With Regular Ground States

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Abstract

We prove general comparison theorems for eigenvalues of perturbed Schrödinger operators that allow proof of Lieb–Thirring bounds for suitable non-free Schrödinger operators and Jacobi matrices.

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Authors and Affiliations

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

    Rupert L. Frank

  2. Mathematics 253-37, California Institute of Technology, Pasadena, CA, 91125, USA

    Barry Simon

  3. Department of Mathematics and Physics, Stuttgart University, Pfaffenwaldring 57, 70569, Stuttgart, Germany

    Timo Weidl

Authors
  1. Rupert L. Frank
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  2. Barry Simon
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  3. Timo Weidl
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Corresponding author

Correspondence to Barry Simon.

Additional information

Communicated by M. Aizenman

Supported in part by NSF Grant DMS-0140592 and U.S.–Israel Binational Science Foundation (BSF) Grant No. 2002068.

Supported in part by DFG grant WE-1964 2/1.

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Frank, R.L., Simon, B. & Weidl, T. Eigenvalue Bounds for Perturbations of Schrödinger Operators and Jacobi Matrices With Regular Ground States. Commun. Math. Phys. 282, 199–208 (2008). https://doi.org/10.1007/s00220-008-0453-1

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  • DOI: https://doi.org/10.1007/s00220-008-0453-1

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