A conjecture for some partial differential operators on \(L^ 2(\mathbb{R}^ n)\)
Selfadjoint partial differential operators of the form \(h(- i \nabla) + (1 + x^2)^{-\delta}\) on \(L^2 (\mathbb{R}^n)\) are studied. Employing the Enss method [\textit{V. Enss}, Commun. Math. Phys. 61, 285-291 (1978; Zbl 0389.47005)] it is shown that the wave operators exist and that their range is the absolutely continuous subspace. This holds for \(h\) in a class of polynomials.
scientific article; zbMATH DE number 729853