 01213 Pavel Exner, Katerina Nemcova
 Bound states in pointinteraction star graphs
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Jun 8, 01

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Abstract. We discuss the discrete spectrum of the
Hamiltonian describing a twodimensional quantum particle
interacting with an infinite family of point interactions. We
suppose that the latter are arranged into a starshaped 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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