Classical solution of the wave equation

Abstract

The classical limit of wave quantum mechanics is analyzed. It is shown that the general requirements of continuity and finiteness to the solution $ψ(x)=Ae^{iϕ(x)}+ Be^{-iϕ(x)}$, where $ϕ(x)=\frac 1\hbar W(x)$ and $W(x)$ is the reduced classical action of the physical system, result in the asymptote of the exact solution and general quantization condition for $W(x)$, which yields the exact eigenvalues of the system.