Since the Nitrogen atom can tunnel from one side of the molecule to the other, there are cross terms in the
Hamiltonian (limiting ourselves to the two symmetric ground states).

We can adjust the phases of the above and below states to make real.

The energy eigenvalues can be found from the usual equation.

Now find the eigenvectors.

These are solved if . Substituting auspiciously, we get.

So the eigenstates are

The states are split by the interaction term.

Feynman goes on to further split the states by putting the molecules in an electric field. This makes the diagonal terms of the Hamiltonian slightly different, like a magnetic field does in the case of spin.

Finally, Feynman studies the effect of Ammonia in an oscillating Electric field, the Ammonia Maser.

Jim Branson 2013-04-22