A pulse containing 10¹³ electrons is approaching a potential step from the + direction as shown in the figure. The step is well approximated by:

Assume that there is no interaction between the electrons.

1. Find the (unnormalized) wave function for each electron in each region.
2. Estimate the number of electrons that will travel in Region I if E = 20 eV and Uo = 18 eV.

Hints: As the electrons are initially travelling along the -x direction, they may travel along the +x direction in Region II only but not in Region I.

6. A pulse containing 10'3 electrons is approaching a potential step from the +x direction as shown in the gure. The step is well approximated by: 4 O 0 for x 0 (Region 1]) Assume that there is no interaction between the electrons. a) Find the (unnormalized) wave function for each electron in each region. b) Estimate the number of electrons that will travel in Region I if E : 20 eV and U0 = 18 eV. Hints: As the electrons are initially travelling along the -x direction, they may travel along the t direction in Region [I only but not in Region I. (13 marks}