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The description of a system's state as a point in its phase space, although mathematically convenient, is thought to be fundamentally inaccurate. In quantum mechanics, the motion degrees of freedom are superseded with the concept of wave function, and operators which correspond to other degrees of freedom have discrete spectra. For example, intrinsic angular momentum operator (which corresponds to the rotational freedom) for an electron or photon has only two eigenvalues. This discreteness becomes apparent when action has an order of magnitude of the Planck constant, and individual degrees of freedom can be distinguished.
The description of a system's state as a point in its phase space, although mathematically convenient, is thought to be fundamentally inaccurate. In quantum mechanics, the motion degrees of freedom are superseded with the concept of wave function, and operators which correspond to other degrees of freedom have discrete spectra. For example, intrinsic angular momentum operator (which corresponds to the rotational freedom) for an electron or photon has only two eigenvalues. This discreteness becomes apparent when action has an order of magnitude of the Planck constant, and individual degrees of freedom can be distinguished.
尽管在数学上很方便，但将系统状态描述为相空间中的一个点，从根本上讲是不准确的。在量子力学中，体系运动状态的自由度被波函数的概念所取代，并且对应于其他自由度的算子具有离散的光谱。例如，电子或光子的本征角动量算子（对应于旋转自由度）只有两个特征值。当运动具有普朗克常数的量级时，这种离散变得非常明显，并且可以区分出各个自由度。
==References==
==References==