2025/03/12 by Duc Hoang Cao, Cao, Duc Hoang
Mathematics · Physics and Astronomy · #Spectral Theory in Mathematical Physics #Quantum Mechanics and Non-Hermitian Physics #Numerical methods in inverse problems
paper · pdf · doi:10.48550/arxiv.2503.09235
We prove sharp upper bounds for eigenvalues of Schrödinger operators on quantum graphs with δ-coupling (also known as Robin) conditions at all vertices. The bounds depend on the geometry of the graph, on the potential, and the strength of the couplings, and as the coupling strengths grow, the dependence on the topology gets weaker, answering a question of Rohleder and Seifert. We obtain those bounds via the variational characterisation, comparing with appropriate linear combinations of eigenfunctions with Dirichlet and Neumann vertex conditions.