Cartan connection arising from the scaling group of the wave function for the Schr\"{o}dinger equation will be presented. This geometric object will be interpreted as a background (vacuum) on which the system evolves. The idea is the generalization of concepts present in de Broglie-Bohm (pilot wave) theory. The connection allows investigating the geometry of the space on which this Schr\"{o}dinger-Cartan connection is constructed. The procedure is general enough for constructing (non-uniquely) torsion-free Cartan connections for general Partial Differential Equations.
Virial-ansätze for the Schrödinger Equation with a symmetric strictly convex potential
Asymptotic Expansion for the Wave Function in a one-dimensional Model of Inelastic Interaction
Smoothness of Wave Functions in Thermal Equilibrium
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