论文标题
一种数值阻尼的振荡器方法，用于约束Schrödinger方程
A numerical damped oscillator approach to constrained Schrödinger equations
论文作者
论文摘要
本文解释并说明了使用一组耦合的动力学方程，在虚拟时间内的二阶使用，该方程将其收敛到具有其他约束的固定schrödinger方程解决方案。我们包括三个定性不同的数值示例：氢原子的径向schrödinger方程；具有退化激发态的二维谐波振荡器；最后是用于旋转状态的非线性schrödinger方程。提出的方法是直观的，具有用于阻尼振荡器的经典力学中的类比，并且易于实现，可以在自己的编码中或用于动态系统的软件。因此，我们发现将其引入量子力学的延续课程或通常在包含计算部分的应用数学课程中。
This article explains and illustrates the use of a set of coupled dynamical equations, second order in a fictitious time, which converges to solutions of stationary Schrödinger equations with additional constraints. We include three qualitative different numerical examples: the radial Schrödinger equation for the hydrogen atom; the two-dimensional harmonic oscillator with degenerate excited states; and finally a non-linear Schrödinger equation for rotating states. The presented method is intuitive, with analogies in classical mechanics for damped oscillators, and easy to implement, either in own coding, or with software for dynamical systems. Hence, we find it suitable to introduce it in a continuation course in quantum mechanics or generally in applied mathematics courses which contain computational parts.
