History and Philosophy of Quantum Mechanics IV: Tunneling Time Calculation

Abstract

Within Bohmian quantum mechanics, all the quantum effects originate from a single source of term called the quantum potential. Thus, by adjusting its contribution in the dynamical equations of motion, Bohmian mechanics can be applicable to all the possible scales of physical domains. Within the standard quantum mechanics, however, no dynamical process is given for tunneling. Thus, calculating expectation values of time from some other related physical processes is the only way to calculate the tunneling time. However, all the standard approaches suggested so far have deep conceptual problems that are serious enough to reject them all. However, under the ontological interpretation, tunneling is nothing but a simple dynamical motion of a particle that actually goes over the barrier with some additional boost from the quantum potential. Since a particle's visual trajectory is readily available, a particle's actual flight-time can be calculated for the entire path in the ontological formulation. On the other hand, the trajectories and the solutions are calculated concurrently as we move along with the ‘fluid elements' in the hydrodynamical formulation.