Year: 2001
Type: article
Abstract: 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.
Authors: P Exner, K Nemcová
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2037696943