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

  • Tony C. Scott
  • Robert Mann
  • Roberto E. Martinez II

DOI: 10.1007/s00200-006-0196-1

Cite this article as:
Scott, T., Mann, R. & Martinez II, R. AAECC (2006) 17: 41. doi:10.1007/s00200-006-0196-1


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.


Implicit FunctionsSchrödinger EquationRelativity

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Tony C. Scott
    • 1
  • Robert Mann
    • 2
    • 3
  • Roberto E. Martinez II
    • 4
  1. 1.Institut für Physikalishe Chemie, RWTH-Aachen, Fachbereich ChemieUniversität Duisburg-Essen, and Zentralinstitut für Angewandte Mathematik (ZAM) Forschungszentrum Jülich GmbHGermany
  2. 2.Department of Physics, Professor of Physics and Applied MathematicsUniversity of WaterlooOntarioCanada
  3. 3.Perimeter Institute for Theoretical PhysicsOntarioCanada
  4. 4.Harvard UniversityCambridgeUSA