A Bound on the Pseudospectrum of the Harmonic Oscillator with Imaginary Cubic Potential

Patrick W. Dondl, Patrick Dorey, Frank Rösler

We are concerned with the non-normal Schrödinger operator $$H=-\Delta +V$$ on $L^2({\mathbb{R}}^n)$, where $V\in W_{\text{loc}}^{1,\infty }({\mathbb{R}}^n)$ and $\operatorname{Re} (V(x))\ge…