We analyze the effects of inelastic scattering on the tunneling time theoretically, using generalized Nelson’s quantum mechanics. This generalization enables us to describe quantum system with channel couplings and optical potential in a real time stochastic approach, which seems to give us a new insight into quantum mechanics beyond Copenhagen interpretation

From the advent of quantum mechanics, various types of stochastic-dynamical approach to quantum mechanics have been tried. We discuss how to utilize Nelson’s stochastic quantum mechanics to analyze the tunneling phenomena, how to derive relativistic field equations via the Poisson process and how to describe a quantum dynamics of open systems by the use of quantum state diffusion, or the stochastic Schrödinger equation.

We construct a tunneling time distribution by means of Nelson’s quantum mechanics and investigate statistical properties of the tunneling time distribution. As a result, we find that the relationship between the average and the variance of the tunneling time shows ‘wave-particle duality’.

A Poisson process is one of the fundamental descriptions for relativistic particles: both fermions and bosons. A generalized linear photon wave equation in dispersive and homogeneous medium with dissipation is derived using the formulation of the Poisson process. This formulation provides a possible interpretation of the passage time of a photon moving in the medium, which never exceeds the speed of light in vacuum.