Semiclassical analysis of low and zero energy scattering for one dimensional Schrödinger operators with inverse square potentials

Ovidiu Costin, Wilhelm Schlag, Wolfgang Staubach +1

This paper studies the scattering matrix $\Sigma (E;\hslash )$ of the problem \[ -\hbar^2 ψ''(x) + V(x) ψ(x) = Eψ(x) \] for positive potentials $V\in C^{\infty }(\mathbb{R})$ with inverse square behav…