Speaker
Description
We study a system where a particle scatter on the periodic Dirac delta potential. The problem is canonical i.e. it is considered during typical quantum mechanics course. There are several approaches to solve the Schrodinger equation for such a systems [1] [2]. However most of solutions rely on different matrix method. We would like to introduce new, combinatorial method by writing system of recursive equations. Based off this solution we write transmission and reflected coefficients of a wave functions of a particle, which is the common way to describe Quantum tunnelling.
The most interesting conclusion from the introduced technique: we reveal combinatorial structure of the typical quantum mechanics problem and write transmission and reflected coefficients using binomial coefficients as the number of combinations with repetition.
[1] Fatih Erman, Manuel Gadella, and Haydar Uncu. On scattering from the one dimensional multiple dirac delta potentials. European Journal of Physics, 39, 01 2018
[2] D. Kiang. Multiple Scattering by a Dirac Comb. American Journal of Physics, 42:785–787, September 1974.
