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arXiv · 1812.06500

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

Sebastian Egger·Joachim Kerner·Konstantin Pankrashkin
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Abstract

In this paper we study an interacting two-particle system on the positive 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.

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Sebastian Egger, Joachim Kerner, Konstantin Pankrashkin. 2018-12-16. Bound states of a pair of particles on the half-line with a general interaction potential. https://doi.org/10.4171/jst%2F331

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