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a=86400 General relativity and quantum mechanics: towards a generalization of the Lambert W function A Generalization of the Lambert W Function | Applicable Algebra in Engineering, Communication and Computing
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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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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.

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Authors and Affiliations

  1. Institut für Physikalishe Chemie, RWTH-Aachen, Fachbereich Chemie, Universität Duisburg-Essen, and Zentralinstitut für Angewandte Mathematik (ZAM) Forschungszentrum Jülich GmbH, Germany

    Tony C. Scott

  2. Department of Physics, Professor of Physics and Applied Mathematics, University of Waterloo, Ontario, Canada, N2L 3G1

    Robert Mann

  3. Perimeter Institute for Theoretical Physics, 31 Caroline Street North, Waterloo, Ontario, Canada, N2L 2Y5

    Robert Mann

  4. Harvard University, 9 Oxford Street, Cambridge, MA, 02138, USA

    Roberto E. Martinez II

Authors
  1. Tony C. Scott
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  2. Robert Mann
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  3. Roberto E. Martinez II
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Correspondence to Tony C. Scott.

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Scott, T., Mann, R. & Martinez II, R. General relativity and quantum mechanics: towards a generalization of the Lambert W function A Generalization of the Lambert W Function. AAECC 17, 41–47 (2006). https://doi.org/10.1007/s00200-006-0196-1

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  • DOI: https://doi.org/10.1007/s00200-006-0196-1

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