General Relativity and Quantum Mechanics: Towards a Generalization of the Lambert W Function

Tony C. Scott, Robert B. Mann

Published 2006-07-09, updated 2006-09-06Version 2

Herein, 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. In particular, this generalization expresses the exact solutions for general-relativistic self-gravitating 2-body and 3-body systems in one spatial and one time dimension. It also expresses the solution to a previously unknown mathematical link between the lineal gravity problem and the Schroedinger equation.