Consider a quantum system with Hamiltonian H and consider the measurement of an observable $a_n$ associated with a different operator A.
Initially the system is an eigenstate $|\phi_n \rangle$ with eigenvalue $a_n$ and we begin to take measurements of the observable A.
We can approximate the probability of measuring an eigenvalue of $a_n$ at time t as:
$$1-t^2( \langle \phi_n| H^2|\phi_n \rangle - \langle \phi_n| H|\phi_n \rangle^2))$$
I am very confused as to where this equation has come from and any guidance to deduce it would be appreciated.