Sample paths in stochastic mechanics: some numerical exercises
Sample paths in stochastic mechanics: some numerical exercises
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随机力学中的示例路径：一些数值练习
DOI：
10.1088/0143-0807/9/1/006
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发表时间：
1988
期刊：
影响因子：
--
通讯作者：
E. Pulignano
中科院分区：
文献类型：
--
作者：
D. Falco;E. Pulignano
尼尔森的随机力学将一个随机过程与薛定谔方程的每个解联系在一起。对于几个简单的例子(高斯波包和高斯波包的叠加)，作者展示了相关Nelson过程的数值生成的样本路径。在这样做的过程中，他们必须解几个随机微分方程式：强调这一目的所需算法的简单性，并且本身就具有一定的教学意义。至于随机力学，他们自己解决的问题是如何从由此产生的样本路径中读取关于量子系统的各种可观察到的信息，获得关于位置和动量的完整答案，以及关于宇称和轨道角动量的部分但令人兴奋的证据。
Nelson's stochastic mechanics associates a stochastic process to each solution of the Schrodinger equation. For a few simple examples (gaussian wavepackets and superpositions of gaussian wavepackets), the authors exhibit numerically generated sample paths of the associated Nelson processes. In doing so, they have to solve a few stochastic differential equations: the simplicity of the algorithm needed for this purpose is emphasised and is of some pedagogical interest by itself. As to stochastic mechanics, they address themselves the question of how to read, from the sample paths thus generated, information about various observables of the quantum system, obtaining complete answers about position and momentum and partial, but stimulating, evidence about parity and orbital angular momentum.