Transmission properties of the one-dimensional array of delta potentials

TL;DR

This paper investigates the transmission properties of a quantum particle interacting with a linear array of delta potentials in a one-dimensional wire, analyzing symmetries, invariances, and conditions for perfect transmission.

Contribution

It introduces a transfer matrix approach to compute transmission probabilities for arbitrary arrays and explores specific symmetries and perfect transmission scenarios.

Findings

Derived transfer matrix for arbitrary N and specific arrays

Identified symmetries and invariances in delta potential arrays

Showed conditions under which perfect transmission occurs

Abstract

The problem of one-dimensional quantum wire along which a moving particle interacts with a linear array of N delta-function potentials is studied. Using a quantum waveguide approach, the transfer matrix is calculated to obtain the transmission probability of the particle. Results for arbitrary N and for specific regular arrays are presented. Some particular symmetries and invariances of the delta-function potential array for the N = 2 case are analyzed in detail. It is shown that perfect transmission can take place in a variety of situations.