含复非线性项的薛定谔方程的Cole-Hopf类变换

对数薛定谔方程的小时间近似可控性

Small-time approximate controllability of the logarithmic Schr\''dinger equation

该论文证明了对数非线性薛定谔方程在双线性控制下的小时间全局近似可控性，通过结合相位控制和梯度流方法，并借助WKB分析处理非线性估计，为首个此类结果。

薛定谔传输的一个实际问题

A practice problem for Schr{ö}dinger transmission

我们提出的情况下，量子传输通过一个光滑的，单件指数的潜力，$V(x)=-V_0 e^{x/a}$，在相反的分段连续的潜力，作为教学模型，以演示传输（反射）系数的解析提取。

Web-Schrödinger: Program for the interactive solution of the time dependent and stationary two dimensional (2D) Schr{ö}dinger equation

Web-Schr{ö}dinger is an interactive client-server software for the solution of the time-dependent and time-independent (stationary) Schr{ö}dinger equation. The program itself runs on a server computer and can be used through the Internet with a simple Web browser. Nothing is installed on the user's computer. The user can load, run, and modify ready-made example files, or prepare her/his own configuration(s), which can be saved on her/his own computer for later use. Several users can access the program parallelly and each can have independent sessions. Typical run times are in the second, or mi…

利用Schr{<$}dinger-Robertson测不准关系通过su（2）和su（1，1）代数的纠缠条件

Entanglement condition via su(2) and su(1,1) algebra using Schr{ö}dinger-Robertson uncertainty relation

薛定谔-罗伯逊不等式通常比海森堡测不准关系对两个非对易观测量的不确定性乘积提供更强的界，因此，它可以结合部分转置产生更严格的可分性条件。本文利用Schr{<$}dinger-Robertson测不准关系，使以前由su（2）和su（1，1）代数导出的可分性条件更加严格，并将其细化为关于局部相移的形式不变.此外，提出了一个线性光学方案来测试这个不变的可分性条件。

Wavefunction collapse induced by gravity in a relativistic Schr{\''o}dinger-Newton model

A relativistic version of the Schr{ö}dinger-Newton equation is analyzed within the recently proposed Grave de Peralta approach [L. Grave de Peralta, {\em Results Phys.} {\bf 18} (2020) 103318], which include relativistic effects by a parametrization of the non-relativistic hamiltonian, so as to impose that the average kinetic energy of the system coincide with its relativistic kinetic energy. The reliability of this method is tested for the particle in a box. By applying this method to the Schr{ö}dinger-Newton equation we shows that the characteristic length of the model [L. Di{ó}si, {\em Phys…

从经典力学和普朗克假设推导薛定谔方程

Straightforward Derivation of the Schr{ö}dinger Equation from Classical Mechanics and the Planck Postulate

根据广泛接受的概念，薛定谔方程（SE）原则上是不可导的。与这种信念相反，我们在这里提出了一个简单的推导SE。它仅基于两个力学基础：经典的哈密顿-雅可比方程（HJE）和关于微观尺度能量离散转移的普朗克假设。我们的方法是从其他出版的衍生SE，要么采用一个特设的基本假设的概率或统计性质的微观现象，或依赖于先验知识的SE，并通过引入一个新的假设来达到它-既不存在于经典力学，也不遵循实验-与一个合适的，但物理上不合理的选择一个关键的任意常数。