Bernard Helffer

collaborators

2 papers

math.SP2010

Semiclassical spectral asymptotics for a two-dimensional magnetic Schrödinger operator: The case of discrete wells

Bernard Helffer, Yuri A. Kordyukov

We consider a magnetic Schrödinger operator $H^{h}$ , depending on the semiclassical parameter $h > 0$ , on a two-dimensional Riemannian manifold. We assume that there is no electric fie…

math.SP2009

Spectral properties of higher order anharmonic oscillators

Bernard Helffer, Mikael Persson

We discuss spectral properties of the self-adjoint operator \[ -d^2/dt^2 + (t^{k+1}/(k+1)-α)^2 \] in $L^{2} (R)$ for odd integers $k$ . We prove that the minimum over $α$ of t…