Resonances as Viscosity Limits for Exterior Dilation Analytic Potentials

For exterior dilation analytic potential, $V$, we use the method of complex scaling to show that the resonances of $- \Delta + V$, in a conic neighbourhood of the real axis, are limits of eigenvalues of $- \Delta + V - i \epsilon x^2$ as $\epsilon \to 0+$, if $V$ can be analytically extended from $\mathbb{R}^n$ to a truncated cone in $\mathbb{C}^n$.