Norm resolvent convergence of singularly scaled Schrödinger operators and δ′-potentials
Norm resolvent convergence of singularly scaled Schrödinger operators and δ′-potentials
For a real-valued function V from the Faddeev-Marchenko class, we prove the norm resolvent convergence, as \epsilon goes to 0, of a family S_\epsilon of one-dimensional Schr\"odinger operators on the line of the form S_\epsilon:= -D^2 + \epsilon^{-2} V(x/\epsilon). Under certain conditions the family of potentials converges in the sense …