Finding wavefunctions for even the simplest of interacting particle systems consisting of two particles is extremely difficult. It is therefore highly desirable that an accurate and easily implementable method be available to instructors and students of quantum-mechanics for obtaining wavefunctions for these particles. The usual approach taken to do this is to use parametrized functional form for the wavefunction in conjunction with the variational method to find approximate wavefunction and energy for the ground-state of such systems. In this paper, we employ random numbers to obtain ground-state wavefunctions and energies of two interacting particles in different one-dimensional potentials. The idea behind using random numbers is to search freely for functions that lead to lower and lower energy, converging eventually to its lowest value. The method presented is easily applicable numerically using a simple algorithm, and the wavefunctions obtained are highly accurate. Thus, the method presented makes study of two interacting particles accessible to instructors and students alike in a transparent manner.

中文翻译：

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使用随机数变分求解与时间无关的薛定谔方程


即使是由两个粒子组成的最简单的相互作用粒子系统，寻找波函数也是极其困难的。因此，非常希望量子力学的教师和学生能够获得一种准确且易于实施的方法来获得这些粒子的波函数。通常采取的方法是使用波函数的参数化函数形式并结合变分方法来找到此类系统基态的近似波函数和能量。在本文中，我们使用随机数来获得不同一维势下两个相互作用粒子的基态波函数和能量。使用随机数背后的想法是自由搜索导致能量越来越低的函数，最终收敛到最低值。该方法使用简单的算法很容易在数值上应用，并且获得的波函数非常准确。因此，所提出的方法使教师和学生能够以透明的方式研究两个相互作用的粒子。