P. Exner

activity

19952023

most citedConvergence of spectra of graph-like thin manifolds

181 citations · 3.2k across the 184 of their papers we have counts for

collaborators

Showing 2011Show all

3 papers · 1 filter

math-ph2011★ 30 cited

On the ground state of quantum graphs with attractive $δ$ -coupling

Pavel Exner, Michal Jex

We study relations between the ground-state energy of a quantum graph Hamiltonian with attractive $δ$ coupling at the vertices and the graph geometry. We derive a necessary and suf…

math-ph2011★ 12 cited

Spectral estimates for a class of Schrödinger operators with infinite phase space and potential unbounded from below

Pavel Exner, Diana Barseghyan

We analyze two-dimensional Schrödinger operators with the potential $∣ x y ∣^{p} - λ (x^{2} + y^{2})^{p / (p + 2)}$ where $p \geq 1$ and $λ \geq 0$ . We show that there is a critical value of $λ$ such…

quant-ph2011★ 4 cited

Inverse scattering problem for quantum graph vertices

Taksu Cheon, Pavel Exner, Ondrej Turek

We demonstrate how the inverse scattering problem of a quantum star graph can be solved by means of diagonalization of Hermitian unitary matrix when the vertex coupling is of the s…

On the ground state of quantum graphs with attractive δ-coupling

Spectral estimates for a class of Schrödinger operators with infinite phase space and potential unbounded from below

Inverse scattering problem for quantum graph vertices

On the ground state of quantum graphs with attractive $δ$ -coupling