On critical points of eigenvalues of the Montgomery family of quartic oscillators

Bernard Helffer, Matthieu Léautaud

We discuss spectral properties of the family of quartic oscillators ${\mathfrak{h}}_{\mathcal{M}}(\alpha )=-\frac{d^2}{d{t}^2}+(\frac{1}{2}{t}^2-\alpha {)}^2$ on the real line, where $α\in…