Generalized Quantum Lagrangian

The paper concerns the formulation of a Lagrangian function compliant with classical, quantum and relativistic outcomes. The literature Lagrangians are reported with modified local Lorentz transformations, or with potentials inferred directly from the relativistic metric or with geometrical meaning. In this paper the Lagrangian is formulated via the concept of quantum uncertainty only, which allows a non-deterministic approach. This theoretical frame is proven useful to merge without additional hypotheses quantum and relativistic outcomes in a straightforward way.