Effects of Two Successive Parity-Invariant Point Interactions on One-Dimensional Quantum Transmission: Resonance Conditions for the Parameter Space

TL;DR

This paper investigates how two successive parity-invariant point interactions affect quantum transmission in one dimension, deriving conditions for perfect resonance based on parameter relations.

Contribution

It introduces a detailed analysis of the parameter space for two point interactions and identifies specific symmetric and anti-symmetric conditions for resonance.

Findings

Resonance occurs under symmetric parameter relations.

Resonance occurs under anti-symmetric parameter relations.

Parameter space is characterized by four parameters on a product of two tori.

Abstract

We consider the scattering of a quantum particle by two independent, successive parity-invariant point interactions in one dimension. The parameter space for the two point interactions is given by the direct product of two tori, which is described by four parameters. By investigating the effects of the two point interactions on the transmission probability of plane wave, we obtain the conditions for the parameter space under which perfect resonant transmission occur. The resonance conditions are found to be described by symmetric and anti-symmetric relations between the parameters.