The cubic nonlinear Schrödinger equation. More precisely, the confining potential is strongly anisotropic; i.e., the trap frequencies in different directions are of different orders of magnitude. This derivation Derivation of an Applied Nonlinear Schrodinger Equation¨ Todd A. Pitts, Mark R. Laine, Jens Schwarz, Patrick K. Rambo and David B. Karelitz Prepared by Sandia National Laboratories Albuquerque, New Mexico 87185 and Livermore, California 94550 Sandia National Laboratories is a multi-program laboratory managed and operated by Sandia Corporation, a wholly owned subsidiary of Lockheed … nonlinear Schrödinger equation in the nonlinear fiber optics formalism. It was a correction that I made to an equation of Quantum Mechanics. It is missing variables that would make it a deterministic Multivariate Equation. A relationship between the definition of stochastic acceleration of a Brownian particle and nonlinear gauge transformations in a wave function description of that particle is obtained. The nonlinear Schrödinger equation with general nonlinearity of polynomial growth and harmonic confining potential is considered. However, one might then wonder why not add on both sides a nonlinear function of the amplitude of the wave, such as κA 2 Z, and arrive at a nonlinear Schrödinger equation of the Gross–Pitaevskii type. Active today. Active today. Viewed 5 times 0 $\begingroup$ I hope this (and not MathOverflow) is the right place to post this question. Vela [ A 51 . Introduction In mathematical physics theory, pulse propagation in an optical fiber is modeled by the nonlinear Schrödinger equation (NLSE) [1–3].

Derivation of nonlinear Schrödinger equation from many-body QM. We propose some nonlinear Schrödinger equations by adding some higher order terms to the Lagrangian density of Schrödinger field, and obtain the Gross-Pitaevskii (GP) equation and the logarithmic form equation naturally. Ask Question Asked today. This book constitutes the first effort to summarize a large volume of results obtained over the past 20 years in the context of the Discrete Nonlinear Schrödinger equation and the physical settings that it describes.

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Schrödinger Equation is a postulate in traditional approaches to Quantum Mechanics. The generic form of the nonlinear Schr¨odinger (NLS) equations is derived from two assumptions which are entirely inde-pendent from the postulates of quantum mechanics. Ask Question Asked today. It i s as smooth as the singularity /U(~-'U u=0 the function allows; i f p is an odd integer it is ern THE NONLINEAR SCIIRdDINGER EQUATION 455 This local existence result follows easily by the standard Picard method. The following sections extend the results of Sections 2 The linear Schrödinger equation, 3 Finite difference schemes for the linear Schrödinger equation, 4 Derivation of the discrete TBC to the cubic nonlinear Schrödinger equation . Derivation of the Schrödinger Equation and the Klein-Gordon Equation from First Principles Gerhard Grössing Austrian Institute for Nonlinear Studies Parkgasse 9, A-1030 Vienna, Austria Abstract: The Schrödinger- and Klein-Gordon equations are directly derived from classical Lagrangians. proof may be found in Ginibre and Theorem 2 - Let X<0 and p 2 1+ 4/n. I think you could postulate Klein-Gordon Equation or Dirac Equation instead, which appeared as relativistic generalizations of Schrödinger Equation, and derive the latter as a Classical Limit of the former(s). I used to not believe that it was a fundamental equation until I realized that I had derived it. Derivation of nonlinear Schrödinger equation from many-body QM.