Bound states in point-interaction star-graphs

Details Bound states in point-interaction star-graphs Bound states in point-interaction star-graphs

2001-06-08

arxiv.org/abs/quant-ph/0106047v1

J. Phys. A34 (2001), 7783-7794

Physics

Quantum Physics

17 pages, LaTeX 2e with 9 eps figures

Scientific paper

10.1088/0305-4470/34/38/306

We 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.

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