薛定谔的Cataplex

Post-Newtonian corrections to Schrödinger equations in gravitational fields

In this paper we extend the WKB-like `non-relativistic' expansion of the minimally coupled Klein--Gordon equation after Kiefer and Singh [1], Lämmerzahl [2] and Giulini and Großardt [3] to arbitrary order in $c^{-1}$, leading to Schrödinger equations describing a quantum particle in a general gravitational field, and compare the results with canonical quantisation of a free particle in curved spacetime, following Wajima et al. [4]. Furthermore, using a more operator-algebraic approach, the Klein--Gordon equation and the canonical quantisation method are shown to lead to the same results for so…

低温下超流He4薄膜中的量子动力学与基本激发

Quantum Dynamics and Elementary Excitations in Superfluid He4 Films at Low Temperatures

本文提出描述低温超流He4薄膜的量子非线性薛定谔方程，导出声子-旋子色散关系，并解析及数值求解出孤子与周期波解，具有重要应用前景。

通过经典声子实现量子力学代数。I：作为牛顿运动方程的薛定谔方程以及作为经典平均值的量子可观测量

Algebra of quantum mechanics via classical phonons. I: The Schrodinger equation as the Newtonian equation of motion and quantum observables as classical averages

通过经典声子模型（Frenkel-Kontorova模型）形式上得到单自旋无粒子的薛定谔方程，从耦合谐振子晶格出发经一系列变换在非相对论极限下将克莱因-戈登方程写成薛定谔方程，还能将经典可观测量重写为量子可观测量。

Helical beams of electrons in a magnetic field: New analytic solutions of the Schrödinger and Dirac equations

We derive new solutions of the Schrödinger, Klein-Gordon and Dirac equations which describe the motion of particles in a uniform magnetic field. In contrast to the well known stationary solutions, our solutions exhibit the behavior of quantum particles which very closely resembles classical helical trajectories. These solutions also serve as an illustration of the meaning of the Ehrenfest theorem in relativistic quantum mechanics.

Klein-Gordon方程Volkov解的性质

On the properties of the Volkov solutions of the Klein-Gordon equation

本文给出了带电粒子在平面波电磁场中的Klein-Gordon方程解在常数时间上的完备性的一个初等证明。我们还回顾了不同形式的正交性和完整性关系以前在文献中提出的，我们讨论了可能性，以构建粒子在平面波激光脉冲作为一个扩展的Volkov解决方案的费曼传播。我们表明，这导致一个严格的理由过渡振幅的表达，目前在文献中使用的，一类激光辅助或激光诱导的过程。

Solving the Schrodinger equation with genetic algorithms: a practical approach

The Schrodinger equation is one of the most important equations in physics and chemistry and can be solved in the simplest cases by computer numerical methods. Since the beginning of the 70s of the last century the computer began to be used to solve this equation in elementary quantum systems, e.g. and in the most complex case a hydrogen-like system. Obtaining the solution means finding the wave function, which allows predicting the physical and chemical properties of the quantum system. However, when a quantum system is more complex than a hydrogen-like system then we must be satisfied with a…