  We study the quantum tunneling of non-relativistic electrons for two
dimensional condensed matter systems. We employ the Levy-Leblond equation
(which is the analogue of the Dirac equation for non-relativistic fermions) and
show that the spin of the particle can be incorporated in the 2D tunneling
problem. We derive the transmission and reflection coefficients of spin up and
down electrons and show that the sum of these coefficients are consistent with
the known results for gapless semiconductors.
