Fig. 2.15 Rectangular potential barrier. where is a right-moving component of i and Electron scattering by a step potential barrier: a simple model to

 

Fig. 2.15 Rectangular potential barrier.

where

 

is a right-moving component of ψ_i and

   

Electron scattering by a step potential barrier: a simple model to illustrate the ideas of reflection and transmission. Consider the step potential barrier shown in Figure 2.14. (a) Write the general solution for the electron wavefunction for each region (I, II). Note that the wavevector will be different in each region. (b) What is the expression for kin each region in terms of the energy of that region? (c) Now let us consider an electron wave in region I traveling towards the barrier with energy E> Uo. We want to determine the fraction of the electron that is reflected and transmitted by the barrier, a very important concept characteristic of all wave phenomena. What are the boundary conditions at x = 0? (d) From the boundary conditions, determine the transmission and reflection probabilities, which are respectively defined as