Dwell Time of Particles in Tunneling Barriers of Arbitrary Shape

For a one-dimensional barrier of arbitrary shape, an expression of the dwell time of tunneling particles has been obtained by subdividing it into infinitesimal rectangular barrier elements and then summing the dwell times spent by particles inside the barrier elements, and the dwell times in a parabolic potential barrier were calculated. The results show that the dwell times are almost independent of the barrier width as it is greater than a characteristic width W_c. This can be ascribed that in the width range beyond W_c, the tunneling probabilities through the barrier elements are very small, thus the times taken to tunnel through them make little contribution to the summation of the dwell times in all the barrier elements.