I have the following problem:
Let $Af = -f'' + uf$ be an unbounded operator where $u \in \mathcal{S}(\mathbb{R};\mathbb{R})$ is in the Schwartz class. The domain of $A$ is the linear subspace $H^2(\mathbb{R})$ of $L^2(\mathbb{R})$.
Show that the continuous specrum $A$ is $[0,\infty)$.
I have already shown that $A$ is self-adjoint and my approach would be to find a Weyl sequence that approximates the solution of the eigenvalue problem. However I am not able to find such a sequence and would be grateful for any idea.