# Transparent Quantum Graphs

## TL;DR

This paper develops a method for designing quantum graphs with transparent branching points using boundary conditions that simplify the analysis of quantum networks, applicable to star and tree topologies.

## Contribution

It introduces a novel approach to derive transparent boundary conditions for quantum graphs, simplifying their analysis and design.

## Key findings

- Derived simple constraints for transparent boundary conditions.
- Applied the method to star and tree quantum graphs.
- Extension to complex topologies is straightforward.

## Abstract

We consider quantum graphs with transparent branching points. To design such networks, the concept of transparent boundary conditions is applied to the derivation of the vertex boundary conditions for the linear Schrodinger equation on metric graphs. This allows to derive simple constraints, which use equivalent usual Kirchhoff-type boundary conditions at the vertex to the transparent ones. The approach is applied to quantum star and tree graphs. However, extension to more complicated graph topologies is rather straight forward.