Related papers: Why is Schrodinger's Equation Linear?
A nonlinear generalisation of Schrodinger's equation is obtained using information-theoretic arguments. The nonlinearities are controlled by an intrinsic length scale and involve derivatives to all orders thus making the equation mildly…
Information measures for relativistic quantum spinors are constructed to satisfy various postulated properties such as normalisation invariance and positivity. Those measures are then used to motivate generalised Lagrangians meant to probe…
It is proposed that the Schrodinger equation for a free point particle has non-linear corrections which depend on the mass of the particle. It is assumed that the corrections become extremely small when the mass is much smaller or much…
It is is explained why physical consistency requires substituting linear observables by nonlinear ones for quantum systems with nonlinear time evolution of pure states. The exact meaning and the concrete physical interpretation are…
A nonlinear Schrodinger equation, that had been obtained within the context of the maximum uncertainty principle, has the form of a difference-differential equation and exhibits some interesting properties. Here we discuss that equation in…
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…
The inexactness of the time-dependent Schr\"odinger equation of a charged particle in an external electromagnetic field is discussed in terms of the damping effect of the radiation. A possible improvement is to add a nonlinear term…
We investigate potential quantum nonlinear corrections to Dirac's equation through its sub-leading effect on neutrino oscillation probabilities. Working in the plane-wave approximation and in the $\mu-\tau$ sector, we explore various…
Trying to combine standard quantum field theories with gravity leads to a breakdown of the usual structure of space-time at around the Planck length, 1.6*10^{-35} m, with possible violations of Lorentz invariance. Calculations of…
We review some recent results on nonlinear Schrodinger equations with potential, with emphasis on the case where the potential is a second order polynomial, for which the interaction between the linear dynamics caused by the potential, and…
Nonlinear modifications of quantum mechanics generically lead to nonlocal effects which violate relativistic causality. We study these effects using the functional Schrodinger equation for quantum fields and identify a type of nonlocality…
There are four reasons why our present knowledge and understanding of quantum mechanics could be regarded as incomplete. Firstly, the principle of linear superposition has not been experimentally tested for position eigenstates of objects…
The aim of this paper is to find the exact solutions of the Schrodinger equation. As is known, the Schrodinger equation can be reduced to the continuum equation. In this paper, using the non-linear Legendre transform the equation of…
Starting from a generic generally covariant classical theory we introduce the logarithmic correction to the quantum wave equation. We demonstrate the emergence of the evolution time from the group of automorphisms of the von Neumann algebra…
Using perturbative methods, we analyse a nonlinear generalisation of Schrodinger's equation that had previously been obtained through information-theoretic arguments. We obtain analytical expressions for the leading correction, in terms of…
If there exists a formulation of quantum mechanics which does not refer to a background classical spacetime manifold, it then follows as a consequence, (upon making one plausible assumption), that a quantum description of gravity should be…
The search for a theory that unifies general relativity and quantum theory has focused attention on models of physics at the Planck scale. One possible consequence of models such as string theory may be that Lorentz invariance is not an…
Many of the technical complications associated with the general theory of relativity ultimately stem from the nonlinearity of Einstein's equation. It is shown here that an appropriate choice of dynamical variables may be used to eliminate…
We study the consistency of having Lorentz invariance as a low energy approximation within the quantum field theory framework. A model with a scalar and a fermion field is used to show how a Lorentz invariance violating high momentum scale,…
Various origins of linear and nonlinear Schrodinger equations are discussed in connection with diffusion, hydrodynamics, and fractal structure. The treatment is mainly expository, emphasizing the quantum potential, with a few new…