Based on the recent construction of a self-adjoint momentum operator for a particle confined in a one-dimensional interval, we extend the construction to arbitrarily shaped regions in any number of dimensions. Different components of the momentum vector do not commute with each other unless very special conditions are met. As such, momentum measurements should be considered one direction at a time. We also extend other results, such as the Ehrenfest theorem and the interpretation of the Heisenberg uncertainty relation to higher dimensions.

中文翻译：

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限制在多维腔内的粒子的自伴动量算子

基于最近对限制在一维区间内的粒子的自伴动量算子的构造，我们将该构造扩展到任意数量维度的任意形状的区域。除非满足非常特殊的条件，否则动量矢量的不同分量不会相互交换。因此，动量测量应一次考虑一个方向。我们还扩展了其他结果，例如埃伦费斯特定理和海森堡不确定性关系与更高维度的解释。