Bound states in point-interaction star-graphs

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dc.creatorExner, Pavel
dc.creatorNemcova, Katerina
dc.date2001-06-08
dc.date.accessioned2026-07-07T06:33:59Z
dc.date.available2026-07-07T06:33:59Z
dc.descriptionWe discuss the discrete spectrum of the Hamiltonian describing a two-dimensional quantum particle interacting with an infinite family of point interactions. We suppose that the latter are arranged into a star-shaped graph with N arms and a fixed spacing between the interaction sites. We prove that the essential spectrum of this system is the same as that of the infinite straight "polymer", but in addition there are isolated eigenvalues unless N=2 and the graph is a straight line. We also show that the system has many strongly bound states if at least one of the angles between the star arms is small enough. Examples of eigenfunctions and eigenvalues are computed numerically.
dc.description17 pages, LaTeX 2e with 9 eps figures
dc.identifierhttps://arxiv.org/abs/quant-ph/0106047
dc.identifierhttp://arxiv.org/abs/quant-ph/0106047
dc.identifierJ. Phys. A34 (2001), 7783-7794
dc.identifierdoi:10.1088/0305-4470/34/38/306
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/99381
dc.subjectQuantum Physics
dc.subjectCondensed Matter
dc.subjectMathematical Physics
dc.titleBound states in point-interaction star-graphs
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