Meromorphic Continuation of Scattering Matrices: Long Range, Stark Case
Denis A. W. White · Communications in Partial Differential Equations · 2008
Long range quantum mechanical scattering in the presence of a constant electric field of strength F > 0 is discussed. It is shown that the scattering matrix, as a function of energy, has a meromorphic continuation to the entire complex plane as a bounded operator on L(ℝ n−1) where n is the space dimension. There is a marked contrast between this result and the comparable result in the Schrödinger case (F = 0). The scattering matrix is constructed using two Hilbert space wave operators and time dependent modified wave operators both and the constructions are compared.