It is shown in Section 6,1 that for the E

It is shown in Section 6,1 that for the E0 potential step, B = —[(α + ik)/(α - ik)]A. Use this to calculate the probability density (including both incident and reflected waves) to the left of the step:

(a)Show that the result is 4 , where θ = tan-1 (k/α). Because the reflected wave is of the same amplitude as the incident, this is a typical standing wave pattern, varying periodically between 0 and 4A*A.

(b)Determine θ and D (the amplitude of the x > 0 wave inside the step) in the limits k → 0 and α → 0, and interpret your results.