A uniqueness theorem for higher order anharmonic oscillators

Søren Fournais, Mikael Persson Sundqvist

We study for $\alpha \in \mathbb{R}$, $k\in \mathbb{N}\setminus \{0\}$ the family of self-adjoint operators \[ -\frac{d^2}{dt^2}+\Bigl(\frac{t^{k+1}}{k+1}-α\Bigr)^2 \] in $L^2(\mathbb{R})$ and show th…