General relativity and quantum mechanics: towards a generalization of the Lambert W function A Generalization of the Lambert W Function

Authors:
Tony C. Scott;Robert Mann;Roberto E. Martinez II
Affiliations:
Institut für Physikalishe Chemie, RWTH-Aachen, Fachbereich Chemie, Universität Duisburg-Essen, and Zentralinstitut für Angewandte Mathematik (ZAM) Forschungszentrum Jül ...;Department of Physics, Professor of Physics and Applied Mathematics, Univ. of Waterloo, Ontario, Canada and Perimeter Inst. for Theoretical Physics, 31 Caroline St. North, Waterloo, Ontario, Canad ...;Harvard University, 9 Oxford Street, 02138, Cambridge, MA, USA
Venue:
Applicable Algebra in Engineering, Communication and Computing
Year:
2006

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Abstract

We present a canonical form for a natural and necessary generalization of the Lambert W function, natural in that it requires minimal mathematical definitions for this generalization, and necessary in that it provides a means of expressing solutions to a number of physical problems of fundamental nature. This generalization expresses the exact solutions for general-relativistic self-gravitating N-body systems in one spatial and one time dimension, and a previously unknown mathematical link between the (1+1) gravity problem and the Schrödinger wave equation.