# Talk by Jon Harrison

On April 26th, 2023, Jon Harrison (Baylor University) gave a talk about **"Quantizing graphs, one way or two?"** as part of the research seminar Analysis of the FernUniversität in Hagen.

## Abstract

Quantum graphs were introduced to model free electrons in organic molecules using a self-adjoint Hamiltonian on a network of intervals. A second model of graph quantization describes wave propagation by specifying unitary scattering matrices at the vertices. A question that is frequently raised is the extent to which these models are the same or complimentary. In the talk I will present some of the results related to this issue. In particular, we observe that a self-adjoint Dirac operator on the graph obtained by restricting the Dirac equation in three dimensions to an interval produces a secular equation for the graph spectrum that matches the secular equation associated with any construction of wave propagation when the Dirac operator describes particles with zero mass and the vertex conditions do not allow spin rotation.