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 Schrodinger equations with additional constraints. We include three qualitative different numerical examples: the radial Schrodinger equation for the hydrogen atom; the two-dimensional harmonic oscillator with degenerate excited states; and finally a non-linear Schrodinger 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.

中文翻译：

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约束薛定谔方程的数值阻尼振荡器方法

本文解释并说明了一组耦合动力学方程的使用，虚拟时间中的二阶，它收敛到具有附加约束的稳态薛定谔方程的解。我们包括三个定性不同的数值例子：氢原子的径向薛定谔方程；具有简并激发态的二维谐振子；最后是旋转状态的非线性薛定谔方程。所提出的方法是直观的，类似于阻尼振荡器的经典力学，并且易于实现，无论是在自己的编码中，还是使用动态系统的软件。因此，我们发现将它引入量子力学的继续课程或通常包含计算部分的应用数学课程中是合适的。