The neutral Kaons,
form a very interesting two state system.
As in the Ammonia molecule, there is a small amplitude to make a transition form one to the other.
The Energy (mass) eigenstates are similar to those in the example above,
but the CP (Charge conjugation times Parity) eigenstates are important because they determine how the particles can decay.
A violation of CP symmetry is seen in the decays of these particles.