  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 A superseded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.
