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math.SP2013★ 13 cited
Approximations of quantum-graph vertex couplings by singularly scaled rank-one operators
Pavel Exner, Stepan Manko
We investigate approximations of the vertex coupling on a star-shaped graph by families of operators with singularly scaled rank-one interactions. We find a family of vertex coupli…
math-ph2013★ 7 cited
Approximations of quantum-graph vertex couplings by singularly scaled potentials
Pavel Exner, Stepan S. Manko
We investigate the limit properties of a family of Schrödinger operators of the form $H_\varepsilon= -\frac{\mathrm{d}^2}{\mathrm{d}x^2}+ \frac{λ(\varepsilon)}{\varepsilon^2}Q \big…