NANOSYSTEMS: PHYSICS, CHEMISTRY, MATHEMATICS, 2017, 8 (1), P. 20–23
On a non-separable quantum many-particle system on the half-line
J. Kerner – Department of Mathematics and Computer Science, FernUniversität in Hagen, 58084 Hagen, Germany; Joachim.Kerner@fernunihagen.de
T. Mühlenbruch – Department of Mathematics and Computer Science, FernUniversität in Hagen, 58084 Hagen, Germany; Tobias.Muehlenbruch@fernunihagen.de
In this paper we will report on a one-dimensional, non-separable quantum many-particle system. It consists of two (distinguishable) particles moving on the half-line R+ being subjected to two different kinds of two-particle interactions: singular many-particle interactions localized at the origin and a binding-potential leading to a molecular-like state. We will formulate the model precisely, obtaining a well-defined self-adjoint operator (the Hamiltonian for our system) and elaborate on its spectral properties. In addition, we will present possible directions for future research.
Keywords: singular many-particle interactions, molecule, spectral analysis, quantum graph.
PACS 03.65.Db, 73.21.Hb, 05.45.Ac