Reflection and transmission resonances and accuracy of the wkb method
arXiv:1302.2403
Abstract
In this paper, we calculate the transmission and reflection amplitudes of wave functions for different potentials such as the delta function, the rectangular barrier, the Eckart potential, and the Hulthen potential. We describe the relationship between these amplitudes and compute the reflection resonances between each potential. We describe the transmission and reflection probabilities using the WKB formula and compare the results with ones obtained from matching the boundary conditions. Furthermore, we use a two by two transfer matrix to calculate a rigorous bound on the transmission and reflection probabilities.
V1: 20 pages, 11 figures, to appear in the proceedings of the 2nd Regional Conference on Applied and Engineering Mathematics (Penang), Malaysia. V2: Minor typos fixed; minor improvements in presentation; no significant change in physics conclusions