Journal
REPORTS ON MATHEMATICAL PHYSICS
Volume 80, Issue 2, Pages 143-151Publisher
PERGAMON-ELSEVIER SCIENCE LTD
DOI: 10.1016/S0034-4877(17)30068-X
Keywords
singular interactions; molecule; discrete spectrum; essential spectrum; quantum graph
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In this paper we provide an extension of the model discussed in [10] describing two singularly interacting particles on the half-line R+. In this model, the particles are interacting only whenever at least one particle is situated at the origin. Stimulated by [11] we then provide a generalisation of this model in order to include additional interactions between the particles leading to a molecular-like state. We give a precise mathematical formulation of the Hamiltonian of the system and perform spectral analysis. In particular, we are interested in the effect of the singular two-particle interactions onto the molecule.
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