Exact Solution for One Dimensional Multibarrier Tunneling

Abstract

Quantum tunneling across multiple barriers as yet is an unsolved problem for barrier numbers greater than five. The complexity of the mathematical analysis even for small number of barriers pushed it into the realms of Numerical Analysis. This work is aimed at providing a rigorously correct solution to the general N barrier problem, where N can be any positive integer. An exact algebraic solution has been presented, which overcomes the complexity of the WKB integrals that are traditionally employed, and matches the earlier results reported for small number of barriers. The solution has been explored to considerable depth and many startling consequences have been pointed out for 500 and 1000 barriers. These are quite revealing and open up many avenues for engineering applications and further research.