Re: paradoxical relation between the ease of flipping and coefficient A

This appears to be degenerate perturbation theory.
There are two benzene states |a> and |b> with the same unperturbed energy
E_0.  There is a small perturbation V that connects the states, 
with A=.  Thus, "the easier the flipping back and forth between the
two states, the higher the coefficient A".
This gives a 2X2 matrix |E_0   A |  
                        | A   E_0|.
The perturbed energies are obtained by diagnolizing this matrix,
resulting in energies E_1=E_0+A and E_2=E_0-A.
Thus, "the higher the coefficient A, the higher the energy separation
between the two states."