Consider a potential step
(6.3) |
Let me define
I assume a beam of particles comes in from the left,
(6.6) |
At the potential step the particles either get reflected back to region I, or are transmitted to region II. There can thus only be a wave moving to the right in region II, but in region I we have both the incoming and a reflected wave,
We define a transmission and reflection coefficient as the ratio of currents between reflected or transmitted wave and the incoming wave, where we have canceled a common factor
(6.9) |
Even though we have given up normalisability, we still have the two continuity conditions. At these imply, using continuity of and ,
We thus find
and the reflection and transmission coefficients can thus be expressed as
Notice that !
In Fig. 6.2 we have plotted the behaviour of the transmission and reflection of a beam of Hydrogen atoms impinging on a barrier of height 2 meV.