A new approach to solving the Schrödinger equation

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。

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。

Implementation of traveling odd Schr$ö$dinger cat states in circuit-QED

We propose a realistic scheme of generating a traveling odd Schr$ö$dinger cat state and a generalized entangled coherent state in circuit quantum electrodynamics (circuit-QED). A squeezed vacuum state is used as initial resource of nonclassical states, which can be created through a Josephson traveling-wave parametric amplifier, and travels through a transmission line. Because a single-photon subtraction from the squeezed vacuum gives with very high fidelity an odd Schr$ö$dinger cat state, we consider a specific circuit-QED setup consisting of the Josephson amplifier creating the traveling res…

内积量子化的非微扰观点：薛定谔方程的高精度解

A Nonperturbative Perspective on Inner Product Quantization: Highly Accurate Solutions to the Schr{ö}dinger Equation

我们设计了一个新的和高精度的量子化程序的内积表示，无论是在配置和动量空间。利用表示$Ψ(ξ) = \sum_{i}a_i[E]ξ^i R_β(ξ)$，对于一个适当的参考函数，$R_β(ξ)$，我们证明了（收敛）零点的系数函数，$a_i[E] = 0$，近似精确的束缚/共振态能量与$i \to \infty$的精度。该方法的有效性被证明是基于希尔行列式量化过程的扩展。我们的方法已被应用，取得了显着的成功，各种量子力学问题。