The probability of potential barrier penetration in the generalized wkB approximation

Н. И. Жирнов

K. Hagino

Н. И. Жирнов

K. Hagino, A. B. Balantekin

Using the method of the local transmission matrix, we generalize the well-known WKB formula for barrier penetrability to multichannel systems. We compare the WKB penetrability with a solution of the coupled-channels equations, and show that the WKB formula works well at energies well below the lowest adiabatic barrier. We also discuss the eigenchannel approach to a multichannel tunneling, which may improve the performance of the WKB formula near and above the barrier.

S. Rajasekar, R. Velusamy

The WKB approximation is a physically intuitive method and makes many connections with intuition about waves and classical mechanics as well as with results from the early days of quantum theory as it leads to the Bohr quantization condition. The WKB method is due to Gregor Wentzel, Hendrik Anthony Kramers and Leon Nicolas Brillouin. The method is applicable for slowly varying potentials, that is, the potentials that change not more than a few wavelengths. The WKB approximation is a physically intuitive method and makes many connections with intuition about waves and classical mechanics as well as with results from the early days of quantum theory as it leads to the Bohr quantization condition. The Schrödinger equation is solved to find the penetration of a square potential barrier. The WKB method is applied to obtain a transmission coefficient for penetration through a barrier.

Н. И. Жирнов, A. A. Sokolov