Tunneling

5
Example 3: Double Well Potential
A common model that is used to represent inversion in molecules like ammonia is the double well potential shown
in Figure 6.
V=V 0
L
x=0
x=a x=c x=d
Figure 6. Double well potential.
This potential mimics the inversion of ammonia through its planar form, illustrated in Figure 7.
(a)
(b)
Figure 7. (a) Inversion motion of ammonia through the planar transition state. (b) Potential energy of
inversion of ammonia as a function of the out-of-plane angle.
Classically, the ammonia molecule in its ground state does not have enough energy to go over the barrier.
Therefore, a classical ammonia molecule would not experience inversion. In quantum mechanics, though, the
ammonia molecule experiences tunneling through the barrier and so undergoes inversion.