Absence of ballistic motion

Abstract

For large classes of Schrödinger operators and Jacobi matrices we prove that ifh has only one point spectrum then for φ₀ of compact support

$$\mathop {\lim }\limits_{t \to \infty } t^{ - 2} \left\| {xe^{ - ith} \phi _0 } \right\|^2 = 0.$$