Hartman Effect from a Geometrodynamic Extension of Bohmian Mechanics

Abstract: This paper presents the derivation of a general solution to the scattering problem of particles incident onto a barrier of constant potential. This solution is constructed through a geometrodynamic approach to Bohmian mechanics, assuming that particles undergo quantum tunneling along geodesic trajectories in an Alcubierre-like spacetime. Furthermore, from this solution, mathematical expressions for the quantum potential, momentum, position, and tunneling time are determined in terms of the spacetime geometry for each relevant region. This allows us to explain the Hartman effect as a consequence of spacetime distortion generated by the quantum potential within the barrier.