Graph neural networks often diffuse information rather than routing it to specific targets, leading to oversmoothing and oversquashing. This seminar introduces an observable based framework inspired by quantum mechanics to directly measure and control signal routing in graphs. We define a signal routing measure via feature location observables, prove why standard spectral GNNs with real valued signals cannot move signal centers, and propose the Schrödinger GNN: a unitary, complex-modulated architecture that induces directional momentum while preserving energy and norms.