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

Herein, we present a canonical form for a natural and necessary generalization of the Lambert 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 generalrelativistic 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 linear gravity problem, the quantum mechanical Schrödinger wave equation whose functional form is related to the classical projectile motion. AMS Numbers: 33E30, 01-01, 01-02 Also related to: 70B05, 81Q05, 83C47, 11A99