Example 2: Consider the step potential function shown below. Assume that a flux of particles is incident on a potential barrier with energy of Vo. The particles are traveling in the x direction and they are originated from x = -oo. The total energy is fixed at E. (i) Let the wavenumbers in regions I and II be k₁ and k₂. Provide expressions for k₁ and k2. (ii) Derive the time-independent wave solutions that apply in each region. (iii) Write the set of equations that result from applying the boundary conditions. (iv) Derive an expression, in terms of the constants k₁ and k₂, for the reflection coefficient R. The reflection coefficient is defined as the ratio of the reflected flux of particles in region to the incident flux in region I. Wto V(x) Incident particles Yo Region I Region II x=0 Figure: The step potential function. I