1201.0150 (U. Klein)

What is the limit $\hbar \to 0$ of quantum theory ?    [PDF]

U. Klein

An analysis is made of the relation between quantum theory and classical mechanics, in the context of the limit $\hbar \to 0$. Several ways in which this limit may be performed are considered. It is shown thatSchr\"odinger's equation for a single particle moving in an external potential $V$ does not, except for special cases, lead, in this limit, to Newton's equation of motion for the particle. This shows that classical mechanics cannot be regarded as the limiting case of quantum mechanics for $\hbar \to 0$.

View original: http://arxiv.org/abs/1201.0150