The neutral K-meson states \(|K°\rangle\) and \(|\bar K°\rangle\) can be expressed in terms of states \(|K_L\rangle\), \(|K_S\rangle\):
where \(|K_L\rangle\) and \(|K_S\rangle\) are states with definite lifetimes \(\tau_L = \frac1{\gamma_L}\) and \(\tau_S = \frac1{\gamma_S}\) and distinct rest energies mLc2 \(\ne\) mSc2. At time t = 0, a meson is produced in the state \(|\psi(t =0)\rangle\) = \(|K°\rangle\). Let the probability of finding the system in state \(|K°\rangle\) at time t be P0(t) and that of finding the system in state \(|\bar K°\rangle\) at time t be P0(t). Find an expression for P0(t) - \(\bar P\)0(t) in terms of \(\gamma _L\), \(\gamma _S\), mLc2 and mSc2. Neglect CP violation.
