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

Tony C. Scott·Robert B. Mann
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Abstract

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.

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Tony C. Scott, Robert B. Mann. 2006-09-06. General Relativity and Quantum Mechanics: Towards a Generalization of the Lambert W Function. https://arxiv.org/abs/math-ph/0607011

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