# Resonant Transmission in One-Dimensional Quantum Mechanics with Two Independent Point Interactions: Full Parameter Analysis

## TL;DR

This paper analyzes the conditions for perfect resonant transmission of a quantum particle through two point interactions in one dimension, exploring the full parameter space of these interactions.

## Contribution

It provides a comprehensive parameter space analysis for resonant transmission in a one-dimensional quantum system with two point interactions, including physical interpretation.

## Key findings

- Identifies conditions for perfect resonant transmission.
- Describes the parameter space of two point interactions.
- Provides physical interpretation of resonance conditions.

## Abstract

We discuss the scattering of a quantum particle by two independent successive point interactions in one dimension. The parameter space for two point interactions is given by $U(2)\times U(2)$, which is described by eight real parameters. We perform an analysis of perfect resonant transmission on the whole parameter space. By investigating the effects of the two point interactions on the scattering matrix of plane wave, we find the condition under which perfect resonant transmission occurs. We also provide the physical interpretation of the resonance condition.