97-145 Marko Robnik, Luca Salasnich

WKB to all orders and the accuracy of the semiclassical quantization (21K, LaTeX) Mar 25, 97

Abstract , Paper (src), View paper (auto. generated ps), Index of related papers

Abstract. We perform a systematic WKB expansion to all orders for a one--dimensional system with potential $V(x)=U_0/\cos^2{(\alpha x)}$. We are able to sum the series to the exact energy spectrum. Then we show that at any finite order the error of the WKB approximation measured in {\em the natural units of the mean energy level spacing} does not go to zero when the quantum number goes to infinity. Therefore we make the general conclusion that the semiclassical approximations fail to predict the individual energy levels within a vanishing fraction of the mean energy level spacing. (J. Phys. A: Math. Gen. 30, 1711-1718 (1997))

Files: 97-145.tex