WKB近似的替代版本与古典性产生的解释
Superseded version of the WKB approximation and explanation of emergence of classicality
摘要：
把极限hbar-->0作为量子力学的经典极限似乎是愚蠢的，因为hbar是一个确定的物理常数，但它被成功地用于推导WKB近似。在经典极限α->0下提出了WKB近似的一个替代版本，其中α =m/M是物体的屏蔽参数，其中m是有效屏蔽层的质量，M是总质量。该方法不仅适用于量子粒子薛定谔方程的近似解，而且适用于纳米粒子薛定谔方程的近似解。此外，该版本表明，纳米粒子的量子化规则可以通过将旧量子理论的玻尔-索末菲量子化规则中的hbar替换为alpha乘以hbar来实现。最重要的是，该版本有助于澄清经典和量子现实之间的本质区别，并理解从量子到经典力学的过渡以及量子力学本身。
英文摘要：
Regarding the limit hbar-->0 as the classical limit of quantum mechanics seems to be silly because hbar is a definite constant of physics, but it was successfully used in the derivation of the WKB approximation. A superseded version of the WKB approximation is proposed in the classical limit alpha-->0 where alpha=m/M is the screening parameter of an object in which m is the mass of the effective screening layer and M the total mass. This version is applicable to not only approximate solution of Schrodinger equation of a quantum particle but also that of a nanoparticle. Moreover, the version shows that the quantization rules for nanoparticles can be achieved by substituting alpha times hbar for hbar in the Bohr-Sommerfeld quantization rules of the old quantum theory. Most importantly, the version helps clarify the essential difference between classical and quantum realities and understand the transition from quantum to classical mechanics as well as quantum mechanics itself.
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