Factorization of the Non-Stationary Schrodinger Operator
arXiv:0704.2304 · doi:10.1007/s00006-007-0039-6
Abstract
We consider a factorization of the non-stationary Schrodinger operator based on the parabolic Dirac operator introduced by Cerejeiras/ Kahler/ Sommen. Based on the fundamental solution for the parabolic Dirac operators, we shall construct appropriated Teodorescu and Cauchy-Bitsadze operators. Afterwards we will describe how to solve the nonlinear Schrodinger equation using Banach fixed point theorem.
Accepted for publication in Advances in Applied Clifford Algebras