Asymptotic completeness for a new class of Stark effect Hamiltonians (Q1084568)

Existence and completeness of the ordinary wave operators is shown for the Stark effect Hamiltonian \(H=-\frac{d^ 2}{dx^ 2}+x+V(x)\) in one dimension with a potential \(V(x)=W''(x)\), where W is a real-valued bounded function with four bounded derivatives. This class of potentials includes some almost-periodic functions and periodic functions with average zero over a period (Stark-Wannier Hamiltonian). The proofs use commutator computations. In the last section asymptotic completeness in the classical scattering theory is shown for the same class of potentials.