JournalsjstVol. 10, No. 4pp. 1413–1444

Bound states of a pair of particles on the half-line with a general interaction potential

  • Sebastian Egger

    Technion - Israel Institute of Technology, Haifa, Israel

  • Joachim Kerner

    FernUniversität in Hagen, Germany

  • Konstantin Pankrashkin

    Carl von Ossietzky Universität Oldenburg, Germany
Bound states of a pair of particles on the half-line with a general interaction potential cover

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Abstract

In this paper we study an interacting two-particle system on the half-line. We focus on spectral properties of the Hamiltonian for a large class of two-particle potentials. We characterize the essential spectrum and prove, as a main result, the existence of eigenvalues below the bottom of it. We also prove that the discrete spectrum contains only finitely many eigenvalues.

Cite this article

Sebastian Egger, Joachim Kerner, Konstantin Pankrashkin, Bound states of a pair of particles on the half-line with a general interaction potential. J. Spectr. Theory 10 (2020), no. 4, pp. 1413–1444

DOI 10.4171/JST/331