Impurity-bound excitons in one and two dimensions

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Abstract

We study three-body Schrödinger operators in one and two dimensions modelling an exciton interacting with a charged impurity. We consider certain classes of multiplicative interaction potentials proposed in the physics literature. We show that if the impurity charge is larger than some critical value, then three-body bound states cannot exist. Our spectral results are confirmed by variational numerical computations based on projecting on a finite dimensional subspace generated by a Gaussian basis.

Original languageEnglish
JournalJournal of Spectral Theory
Volume10
Issue number3
Pages (from-to)1103-1138
Number of pages36
ISSN1664-039X
DOIs
Publication statusPublished - 2020

Keywords

  • Eigenvalues
  • Excitons
  • Feschbach-schur formula

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