The aim of the famous Born and Jordan 1925 paper was to put Heisenberg’s matrix mechanics on a firm mathematical basis. Born and Jordan showed that if one wants to ensure energy conservation in Heisenberg’s theory it is necessary and sufficient to quantize observables following a certain ordering rule. One apparently unnoticed consequence of this fact is that Schrödinger’s wave mechanics cannot be equivalent to Heisenberg’s more physically motivated matrix mechanics unless its observables are quantized using this rule, and not the more symmetric prescription proposed by Weyl in 1926, which has become the standard procedure in quantum mechanics. This observation confirms the superiority of Born–Jordan quantization, as already suggested by Kauffmann. We also show how to explicitly determine the Born–Jordan quantization of arbitrary classical variables, and discuss the conceptual advantages in using this quantization scheme. We finally suggest that it might be possible to determine the correct quantization scheme by using the results of weak measurement experiments.

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Born-Jordan 量化和薛定谔和海森堡图片的等价

著名的 Born 和 Jordan 1925 论文的目的是将海森堡的矩阵力学建立在牢固的数学基础上。Born 和 Jordan 表明，如果要确保海森堡理论中的能量守恒，则必须且充分地按照一定的排序规则对可观测值进行量化。这一事实的一个明显未被注意的结果是，薛定谔的波动力学不能等同于海森堡的更具物理动机的矩阵力学，除非它的可观测量使用这一规则量化，而不是 Weyl 在 1926 年提出的更对称的处方，后者已成为标准程序量子力学。正如考夫曼已经提出的那样，这一观察证实了 Born-Jordan 量化的优越性。我们还展示了如何明确确定任意经典变量的 Born-Jordan 量化，并讨论使用这种量化方案的概念优势。我们最终建议通过使用弱测量实验的结果来确定正确的量化方案是可能的。