13-50 Pavel Exner and Stepan S. Manko

Approximations of quantum-graph vertex couplings by singularly scaled potentials (216K, pdf) Jun 4, 13

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Abstract. We investigate the limit properties of a family of Schr\"odinger operators of the form $H_arepsilon= -rac{\mathrm{d}^2}{\mathrm{d}x^2}+ rac{\lambda(arepsilon)}{arepsilon^2}Q ig(rac{x}{arepsilon}ig)$ acting on $n$-edge star graphs with Kirchhoff conditions imposed at the vertex. The real-valued potential $Q$ is supposed to have compact support and $\lambda(

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