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)]

摘要

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