Weakly coupled states on branching graphs

DOI10.1007/BF00398355zbMath0861.35068arXivfunct-an/9512001MaRDI QIDQ1816428

Pavel Exner

Publication date: 19 May 1997

Published in: Letters in Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/funct-an/9512001

zbMATH Keywords

number of bound stateslocally integrable potentialsingle negative eigenvalue

Mathematics Subject Classification ID

Estimates of eigenvalues in context of PDEs (35P15) PDEs in connection with quantum mechanics (35Q40) Perturbation theories for operators and differential equations in quantum theory (81Q15)

Related Items (18)

Kagome network with vertex coupling of a preferred orientation ⋮ Schrödinger operators on regular metric trees with long range potentials: weak coupling behavior ⋮ Symmetries of quantum graphs and the inverse scattering problem ⋮ Inverse Sturm-Liouville problem for a star graph by three spectra ⋮ Ambarzumian's theorem for a Sturm-Liouville boundary value problem on a star-shaped graph ⋮ Weakly coupled bound state of 2-D Schrödinger operator with potential-measure ⋮ Recovering the shape of a quantum graph ⋮ Quantum graphs: Coulomb-type potentials and exactly solvable models ⋮ Approximations of quantum-graph vertex couplings by singularly scaled rank-one operators ⋮ APPROXIMATIONS OF SINGULAR VERTEX COUPLINGS IN QUANTUM GRAPHS ⋮ The von Neumann way to treat systems of mixed dimensionality ⋮ Constrained energy minimization and orbital stability for the NLS equation on a star graph ⋮ Quantum graph as a quantum spectral filter ⋮ Inverse Sturm–Liouville problem on equilateral regular tree ⋮ On the existence of point spectrum for branching strips quantum graph ⋮ A single-mode quantum transport in serial-structure geometric scatterers ⋮ THE PRIME GEODESIC THEOREM AND QUANTUM MECHANICS ON FINITE VOLUME GRAPHS: A REVIEW ⋮ The spectral shift function and Levinson's theorem for quantum star graphs

Cites Work

• Unnamed Item
• On the bound state of Schrödinger operators in one dimension
• Free quantum motion on a branching graph
• The bound state of weakly coupled Schrödinger operators in one and two dimensions
• Bargmann's inequalities in spaces of arbitrary dimension
• THE MULTIDIMENSIONAL SCHRÖDINGER OPERATOR WITH A PERIODIC POTENTIAL
• The free Dirac operator on compact and noncompact graphs
• Contact interactions on graph superlattices
• Quantum mechanics of multi-prong potentials
• Quantum mechanics on graphs

This page was built for publication: Weakly coupled states on branching graphs