Asymptotics of scattering phases for the Schrödinger operator with magnetic fields (Q1382859)

The authors consider the Schrödinger operator in \(\mathbb{R}^d\) with magnetic field: \(\sum_{j=1}^{d} (i\partial_j +b_j (x))^2 +q(x).\) Under appropriate assumptions on the behaviour of the functions \(b_j (x)\) and \(q(x)\) at infinity, they give asymptotic formulas for the scattering phases. In particular, the main terms of the asymptotics depend only on the asymptotics at infinity of the even part of the scalar potential \(q\), and odd part of the vector potential \(b_j\). Thus the results of Yafaev are extended to the case of Schrödinger operators with magnetic field.