Scattering of a one-dimensional particle by a potential barrier

V.V. Babikov, K. K. Musabaev

K. K. Musabaev

G. F. Drukarev

P. R. Berman, Alberto G. Rojo

Scattering of non-interacting, identical bosons or fermions by a one-dimensional Dirac delta function barrier potential underlines the importance of the role of statistics (that is, whether the particles obey Fermi–Dirac or Bose–Einstein statistics) in the scattering. We consider an initial wave function for the system that corresponds to one particle incident from the left and one from the right of the potential barrier. For bosons, both particles are scattered either to the left or to the right if the intensity reflection coefficient is 1/2, provided the left and right propagating wave packets fully overlap in the scattering region. For fermions, the particles “pass through” one another, provided the left and right propagating wave packets fully overlap in the scattering region, with zero probability that both particles are scattered to the left or right, consistent with the Pauli exclusion principle.

Florian A. Scheck

Solomon J. Glass, H. Mendlowitz

A Dirac particle scattered by a potential barrier varying in one dimension is treated. The incident momentum is three-dimensional. It is shown that the scattered amplitudes have contributions due to spin-flip.