Some thoughts on an information-theoretic motivated nonlinear Schrodinger equation
Abstract
Description
I begin by reviewing the arguments leading to a nonlinear generalisation of Schrodinger's equation within the context of the maximum uncertainty principle. Some exact and perturbative properties of that equation are then summarised: those results depend on a free regulating/interpolation parameter $η$. I discuss here how one may fix that parameter using energetics. Other issues discussed are, a linear theory with an external potential that reproduces some unusual exact solutions of the nonlinear equation, and possible symmetry enhancements in the nonlinear theory.
8 pages. Presented at the Nonlinearity IV workshop held at Gallipoli, Italy, June 2006. To appear in proceedings
8 pages. Presented at the Nonlinearity IV workshop held at Gallipoli, Italy, June 2006. To appear in proceedings