Abstract—

A numerical method proposed in the authors’ previous work to solve the Schrödinger equation is developed. Ambiguity remains in the method described earlier in identifying the average positions of quantum particles in a molecular system, which were prescribed from external considerations without taking into account the Schrödinger equation itself. In this paper, a list of procedures for the numerical identification of the average positions (scattering centers) of particles in an arbitrary molecular system is given to subsequently apply the Monte Carlo algorithm for solving the corresponding Schrödinger equation. Several examples of using the proposed numerical procedures for calculating molecular systems including the hydrogen atom, the hydrogen molecule, water, benzene (in several modifications), and hypothetical multihydrogen are considered.

中文翻译：

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重建分子系统中量子粒子平均位置的数值方法

摘要——

开发了作者先前工作中提出的求解薛定谔方程的数值方法。在确定分子系统中量子粒子的平均位置时，前面描述的方法仍然存在歧义，这是从外部考虑规定的，没有考虑薛定谔方程本身。在本文中，给出了对任意分子系统中粒子的平均位置（散射中心）进行数值识别的程序列表，以便随后应用蒙特卡罗算法来求解相应的薛定谔方程。考虑了使用提议的数值程序计算分子系统的几个例子，包括氢原子、氢分子、水、苯（在几个修改中）和假设的多氢。