Classical solution of the wave equation

preprint2001arXivOpen access

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)=Aeiϕ(x)+Be−iϕ(x)ψ(x)=Ae^{iϕ(x)}+ Be^{-iϕ(x)}, where ϕ(x)=1ℏW(x)ϕ(x)=\frac 1\hbar W(x) and W(x)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)W(x), which yields the exact eigenvalues of the system.

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