Some thoughts on an information-theoretic motivated nonlinear Schrodinger equation

薛定谔的猫的生平与纠缠历险

The life and entangled adventures of Schrodinger's cat

本文面向普通听众介绍薛定谔的思想实验，展示将量子理论形式体系（特别是叠加概念）扩展至亚原子范围之外的奇异结果，用形式逻辑理解叠加，并追溯其后续发展及实际实验实现。

The large nonlinearity scale limit of an information-theoretically motivated nonlinear Schrodinger equation

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 the regime where the nonlinearity length scale is large compared to the deBroglie wavelength; just as in the perturbative regime, the equation again displays some universality. We also briefly discuss stationary solutions to a naturally induced discretisation of that equation.

Universality in an Information-theoretic Motivated Nonlinear Schrodinger Equation

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 the nonlinearity scale, to the energy eigenvalues of the linear Schrodinger equation in the presence of an external potential and observe some generic features. In one space dimension these are: (i) For nodeless ground states, the energy shifts are subleading in the nonlinearity parameter compared to the shifts for the excited states, (ii) the shifts for the…

An alternative theoretical approach to describe planetary systems through a Schrodinger-type diffusion equation

In the present work we show that planetary mean distances can be calculated with the help of a Schrodinger-type diffusion equation. The obtained results are shown to agree with the observed orbits of all the planets and of the asteroid belt in the solar system, with only three empty states. Furthermore, the equation solutions predict a fundamental orbit at 0.05 AU from solar-type stars, a result confirmed by recent discoveries. In contrast to other similar approaches previously presented in the literature, we take into account the flatness of the solar system, by considering the flat solutions…

球坐标下Schrödinger-Dunkl框架中的信息论度量

Information theoretic measures within Schrödinger-Dunkl framework in spherical coordinates

本文在球坐标下解析求解含Deng-Fan势的Schrödinger-Dunkl方程，获得双原子分子振转能级及多种信息论度量，解析与数值偏差极小。

Why is Schrodinger's Equation Linear?

Information-theoretic arguments are used to obtain a link between the accurate linearity of Schrodinger's equation and Lorentz invariance: A possible violation of the latter at short distances would imply the appearance of nonlinear corrections to quantum theory. Nonlinear corrections can also appear in a Lorentz invariant theory in the form of higher derivative terms that are determined by a length scale, possibly the Planck length. It is suggested that the best place to look for evidence of such quantum nonlinear effects is in neutrino physics and cosmology.