普朗克常数在经典理论和量子理论中的对比作用
The Contrasting Roles of Planck's Constant in Classical and Quantum Theories
摘要：
我们追溯普朗克常数在物理学中的历史出现，我们注意到，最初这个常数并没有与量子联系起来。此外，我们强调，普朗克常数可以出现在经典和量子理论。在这两种理论中，普朗克常数确定了原子现象的尺度。然而，在理论基础中所起的作用是截然不同的。在量子理论中，普朗克常数对理论的结构至关重要。另一方面，在经典电动力学中，普朗克常数是可选的，因为它只作为（均匀）无源贡献的比例因子出现在麦克斯韦方程的一般解中。由于经典电动力学可以在将溶液中的均匀无源贡献取为零或非零的情况下求解，因此自然存在两种不同的经典电动力学理论，一种是普朗克常数取为零，另一种是普朗克常数取为非零。经典电磁学的教科书只提供普朗克常数为零的版本。
英文摘要：
We trace the historical appearance of Planck's constant in physics, and we note that initially the constant did not appear in connection with quanta. Furthermore, we emphasize that Planck's constant can appear in both classical and quantum theories. In both theories, Planck's constant sets the scale of atomic phenomena. However, the roles played in the foundations of the theories are sharply different. In quantum theory, Planck's constant is crucial to the structure of the theory. On the other hand, in classical electrodynamics, Planck's constant is optional, since it appears only as the scale factor for the (homogeneous) source-free contribution to the general solution of Maxwell's equations. Since classical electrodynamics can be solved while taking the homogenous source-free contribution in the solution as zero or non-zero, there are naturally two different theories of classical electrodynamics, one in which Planck's constant is taken as zero and one where it is taken as non-zero. The textbooks of classical electromagnetism present only the version in which Planck's constant is taken to vanish.
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