A Novel Transfer Matrix Framework for Multiple Dirac Delta Potentials

Abstract: We present an analytical framework for studying quantum tunneling through multiple Dirac delta potential barriers in one dimension. Using the transfer matrix method, we derive a closed-form expression for the total transfer matrix of a system composed of $N$ equally spaced delta barriers. In a systematic manner, a compact expression is obtained for the first element of the transfer matrix, based on triangular numbers. This, in turn, allows us to compute the transmission coefficient exactly as a function of the number of barriers. The proposed method successfully reproduces well-known results for one and two barriers and efficiently captures complex interference effects for larger values of $N$, such as $N=4$.