2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/91893In this short paper I discuss how conformal geometric algebra models for euclidean and minkowski targetspaces determine the allowed quantum mechanical statespaces for free particles. I explicitly treat 2-dimensional euclidean space and (1+1)-dimensional spacetime.6 pages, submitted for publicationQuantum PhysicsHigh Energy Physics - TheoryFree particle states from Geometrytext