General relativity and quantum mechanics: towards a generalization of the Lambert W function A Generalization of the Lambert W Function
- First Online:
- 379 Downloads
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.
KeywordsImplicit Functions Schrödinger Equation Relativity
Unable to display preview. Download preview PDF.
- 1.Abramowitz, M., Stegun, I.A.: Handbook of mathematical functions. (9th printing), Dover, New York, 1970Google Scholar
- 2.Arfken, G.B.: Mathematical methods for physicists, 2nd ed., Academic Press, New York, 1970Google Scholar
- 3.Luke, Y.L.: The special functions and their approximations. Vol. 1, Academic Press, New York, 1969Google Scholar
- 10.Martinez II, R.E.: Irrationality from tetration. in preparation, (2005)Google Scholar
- 12.Malecki, J.J., Mann, R.B.: Phys. Rev. E. 69, 1–26 (2004)Google Scholar
- 13.Campbell, S.A.: Dynamics of continuous discrete and impulsive systems. 5, 225–235 (1999)Google Scholar
- 15.Imambekov, A., Demler, E.: Exactly solvable one-dimensional Bose-Fermi mixture. private communication, 2005Google Scholar
- 16.Mann, R.B., Scott, T.C., Martinez, R.E.: Lineal gravity and the Schroedinger wave equation. in preparation, 2005Google Scholar
- 17.Scott, T.C., Aubert-Frécon, M., Grotendorst, J.: New approach for the electronic energies of the hydrogen molecular ion, Chem. Phys., in press (2005)Google Scholar