181 citations · 3.2k across the 184 of their papers we have counts for
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Bound-state asymptotic estimates for window-coupled Dirichlet strips and layers
Pavel Exner, Simeon Vugalter
We consider the discrete spectrum of the Dirichlet Laplacian on a manifold consisting of two adjacent parallel strips or planar layers coupled by a finite number N of windows in th…
Bound states in a locally deformed waveguide: the critical case
P. Exner, S. A. Vugalter
We consider the Dirichlet Laplacian for a strip in with one straight boundary and a width , where is a smooth function of a compact support with a…
Weakly coupled states on branching graphs
Pavel Exner
We consider a Schrödinger particle on a graph consisting of links joined at a single point. Each link supports a real locally integrable potential ; the self--adjo…
A duality between Schroedinger operators on graphs and certain Jacobi matrices
Pavel Exner
The known correspondence between the Kronig-Penney model and certain Jacobi matrices is extended to a wide class of Schroedinger operators on graphs. Examples include rectangular l…
Contact interactions on graph superlattices
Pavel Exner
We consider a quantum mechanical particle living on a graph and discuss the behaviour of its wavefunction at graph vertices. In addition to the standard (or delta type) boundary co…