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General relativity and quantum mechanics: towards a generalization of the Lambert W function A Generalization of the Lambert W Function |
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| Authors: | Tony C. Scott Robert Mann Roberto E. Martinez II |
| Affiliation: | 1. Institut für Physikalishe Chemie, RWTH-Aachen, Fachbereich Chemie, Universit?t Duisburg-Essen, and Zentralinstitut für Angewandte Mathematik (ZAM) Forschungszentrum Jülich GmbH, Germany 2. Department of Physics, Professor of Physics and Applied Mathematics, University of Waterloo, Ontario, Canada, N2L 3G1 3. Perimeter Institute for Theoretical Physics, 31 Caroline Street North, Waterloo, Ontario, Canada, N2L 2Y5 4. Harvard University, 9 Oxford Street, Cambridge, MA, 02138, USA |
| 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. |
| Keywords: | Implicit Functions Schr?dinger Equation Relativity |
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