- #1

randybryan

- 52

- 0

The wave function of an electron of mass m incident to the step from x = -∞ with energy E < V is = e

^{ikx}+ ρe

^{-ikx}for x≤0, and ψ=τe

^{-κx}for x > .

Now consider an electron of the same energy incident from x=-∞ to a barrier of width L consisting of two potential steps described by U(x)=0 for x≤0 and U(x)=V for 0 < x ≤ L, U(x) = 0, for x > L. The electron can be considered to undergo multiple reflections within the barrier before being transmitted. Show that the amplitude for transmission through the barrier after a single pass is

t

_{1}= (1 + ρ)e

^{-κL}(1 - ρ)

and after a double pass with two reflections

t

_{2}=(1 + ρ)e

^{-κL}(-ρ)e

^{-κL}(-ρ)e

^{-κL}(1 - ρ)

I assumed I worked out the Transmission coefficient T = 1 - R at x=0 and x=L and square-root to get the transmission amplitudes, but this does not seem to be working. If anyone can shed any light, I would be much grateful. I could write out my scribbles and attempts, but it would be pretty fruitless as they're not taking me anywhere