General relativity and quantum mechanics: towards a generalization of the Lambert W function A Generalization of the Lambert W Function
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- Scott, T., Mann, R. & Martinez II, R. AAECC (2006) 17: 41. doi:10.1007/s00200-006-0196-1
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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.