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

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.

V1: A generalization to the Lambert W function is suggested with applications to quantum chemistry and general relativity. V2: Changed content/authors, references removed

References in corpus (4)

• Exactly solvable case of a one-dimensional Bose-Fermi mixture
• New Approach for the Electronic Energies of the Hydrogen Molecular Ion
• Exact Solution for the Metric and the Motion of Two Bodies in (1+1) Dimensional Gravity
• 3-Body Dynamics in a (1+1) Dimensional Relativistic Self-Gravitating System

Cited by in corpus (8)

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• Some physical applications of generalized Lambert functions
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• Geodesic congruences in warped spacetimes
• On the generalization of the Lambert $W$ function with applications in theoretical physics
• Self-products of rationally elliptic spaces and inequalities between the ranks of homotopy and homology groups