JournalsjstVol. 7, No. 3pp. 659–697

Pseudospectra of the Schrödinger operator with a discontinuous complex potential

  • Raphaël Henry

    Université Paris-Sud, Orsay, France
  • David Krejčiřík

Pseudospectra of the Schrödinger operator with a discontinuous complex potential cover

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Abstract

We study spectral properties of the Schrödinger operator with an imaginary sign potential on the real line. By constructing the resolvent kernel, we show that the pseudospectra of this operator are highly non-trivial, because of a blow-up of the resolvent at infinity. Furthermore, we derive estimates on the location of eigenvalues of the operator perturbed by complex potentials. The overall analysis demonstrates striking differences with respect to the weak-coupling behaviour of the Laplacian.

Cite this article

Raphaël Henry, David Krejčiřík, Pseudospectra of the Schrödinger operator with a discontinuous complex potential. J. Spectr. Theory 7 (2017), no. 3, pp. 659–697

DOI 10.4171/JST/174