IJPAM: Volume 42, No. 2 (2008)

MEROMORPHIC CONTINUATION OF
THE SCATTERING MATRIX

Denis A.W. White
Department of Mathematics
University of Toledo
Toledo, Ohio, 43606-3390, USA
e-mail: dawhite@math.utoledo.edu


Abstract.Long range quantum mechanical scattering in $\mathbb{R}^n$ in the presence of a constant electric field of strength $F>0$ is discussed. The scattering matrix, as a function of energy, is shown to have a meromorphic continuation to the entire complex plane as a bounded operator on $L(\mathbb{R}^{n-1})$. This result differs from the comparable result in the Schrödinger case ($F=0$).

Received: August 17, 2007

AMS Subject Classification: 35P25

Key Words and Phrases: Schrödinger, stark, long range

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2008
Volume: 42
Issue: 2