Most introductory books on quantum mechanics discuss the particle-in-a-box problem through solutions of the Schrodinger equation, at least, in the one-dimensional case. When introducing the virial theorem, however, its discussion in the context of this simple model is not considered and students ponder the question of the validity of the virial theorem for a system with, apparently, no forces. In this work, we address this issue by solving the particle in a finite box and show that the virial theorem is fulfilled when the appropriate Cauchy boundary conditions are taken into account. We also illustrate how, in the limit of the infinite potential box, the virial theorem holds as well. As a consequence, it is possible to determine the averaged force exerted by the walls on the particle. Finally, a discussion of these results in the classical limit is provided.

中文翻译：

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关于盒子中粒子的维里定理：解释柯西边界条件

大多数关于量子力学的介绍性书籍通过薛定谔方程的解来讨论盒中粒子问题，至少在一维情况下是这样。然而，在介绍维里定理时，没有考虑在这个简单模型的背景下进行的讨论，学生们思考维里定理对于一个显然没有力的系统的有效性问题。在这项工作中，我们通过在有限框中求解粒子来解决这个问题，并表明当考虑到适当的柯西边界条件时，维里定理得到满足。我们还说明了在无限势箱的极限中，维里定理如何也成立。因此，可以确定壁对粒子施加的平均力。最后，