Computing Schrödinger propagators on Type-2 Turing machines

Authors:
Klaus Weihrauch;Ning Zhong
Affiliations:
University of Hagen, 58084 Hagen, Germany;University of Cincinnati, Cincinnati, OH 45221, USA
Venue:
Journal of Complexity
Year:
2006

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Abstract

We study Turing computability of the solution operators of the initial-value problems for the linear Schrodinger equation u"t=i@Du+@f and the nonlinear Schrodinger equation of the form iu"t=-@Du+mu+|u|^2u. We prove that the solution operators are computable if the initial data are Sobolev functions but noncomputable in the linear case if the initial data are L^p-functions and p2. The computations are performed on Type-2 Turing machines.