New boundary conditions in tunneling

Abstract

Via the hydrodynamical formulation of quantum mechanics, we propose new boundary conditions to the problem of tunneling through sharp-edged potential barriers with and without dissipation. Above all, these boundary conditions can be matched without assuming continuity of the wave function at a surface σ where the potential undergoes a finite jump. Our approach yields a general expression for transmission probability from which tunneling with and without dissipation can be directly correlated to standard discussions found in textbooks.