The potential barrier in classical mechanics

D. Sen, A. N. Basu, S. Sengupta

Mark R. A. Shegelski, Erik V. Kozijn

For smooth potential barriers, we compare the quasi-classical tunneling time with an expression that gives a fully quantum mechanical tunneling time. The expression we choose for the quantum mechanical tunneling time is one that has heuristic value. We report results wherein this quantum mechanical tunneling time and the quasi-classical time differ significantly, both quantitatively and qualitatively. To determine the reasons for these differences, we compare the trends in the two times that result from varying the potential. Our findings suggest that, for smooth potential barriers, the quasi-classical tunneling time is unreliable for many cases where it is employed. PACS Nos.: 03.65Xp, 03.65-w

Thomas Strohm

Shiping Yang

The quantum motion of one particle which is in a one-dimensional infinite well which exists a potential barrier have been studied.From the statistical analysis of energy spectra,the nonintegrable phenomenon is in quantum mechanics,but this model in the classical is integrable.The reason for that is the tunneling in quantum mechanics.The degree of noninteger is related to the form of the potential barrier.The more complex the potential barrier is,the more clearly the chaos is.

G.C. Stey