LECTURE 19 BARRIER PENETRATION TUNNELING PHENOMENA PHYSICS 420 SPRING 2006 Dennis Papadopoulos

Fig. 7-1, p.232

We’ve learned about this situation: the finite potential well… …but what if we “turn it upside down”? This is a finite potential barrier. When we solved this problem, our solutions looked like this… IIIIII U -L/2L/2 E What would you expect based on your knowledge of the finite box?

Fig. 7-5, p.238

(in actuality the light field in the optically dense space is evanescent, i.e. exponentially decaying)

Below, the thick curves show the reflectance as the thickness of the low-index layer (air) changes from 10 to 900 nm. Note that as the layer thickness increases, the reflectance becomes closer to total at 41 degrees. That is, FTR gives way to TIR.

Qualitatively:

(pure momentum states) to the left of the barrier to the right of the barrier Instructive to consider the probability of transmission and reflection… R+T=1 of course…

E -U U(x)=-e e x x e 0

U(r) r E R kinetic energy of escaping alpha particle Separation of centers of alpha and nucleus at edge of barrier9.1 fm Height of barrier26.4 MeV Radius at which barrier drops to alpha energy26.9 fm Width of barrier seen by alpha17.9 fm Alpha's frequency of hitting the barrier1.1 x 10^21/s