Paper detail

Comment on "The quantum mechanics of electric conduction in crystals," by R. J. Olsen and G. Vignale [Am. J. Phys. 78 (9), 954-960 (2010)]

In this note we use the notion of time-delay to explain the physical content of the transformation properties of transmission and reflection amplitudes, as a result of a displacement of the potential. Then, we reconsider the recent analysis of the scattering problem by a finite-periodic potential, by Olsen and Vignale, to obtain the total reflection condition in the limit of an infinite number of cells. In doing this, we obtain an expression of Hartman's effect, showing that the group velocity of the transmitted particle inside the potential chain can become arbitrary large, as the number of cells tends to infinity.