We use a discrete derivative to introduce a time operator for non-relativistic quantum systems with point spectrum. The symmetry requirement on the time operator leads to well-defined time values related to the dynamics of discrete quantum systems. As an illustration, we find travel times between hits with the walls for the quantum particle in a box model. These times suggest a classical analog of time eigenstates. We also briefly consider the Woods–Saxon potential and propose classical analogs for it.

中文翻译：

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离散的自伴和量子动力学。出行时间

我们使用离散导数为具有点谱的非相对论量子系统引入时间算子。时间算符的对称性要求导致与离散量子系统动力学相关的定义明确的时间值。作为说明，我们发现了盒模型中量子粒子壁之间的碰撞之间的传播时间。这些时间暗示了时间本征态的经典模拟。我们还简要地考虑了伍兹-撒克逊人的潜力，并提出了经典的类似物。