Schrödinger operators on star graphs with singularly scaled potentials supported near the vertices
Schrödinger operators on star graphs with singularly scaled potentials supported near the vertices
We study Schrödinger operators on star metric graphs with potentials of the form αɛ−2Q(ɛ−1x). In dimension 1 such potentials, with additional assumptions on Q, approximate in the sense of distributions as ɛ → 0 the first derivative of the Dirac delta-function. We establish the convergence of the Schrödinger operators in …