The Mandelstam–Tamm limit can also be stated for mixed states and for time-varying Hamiltonians. In this case, the Bures metric must be employed in place of the Fubini–Study metric. A mixed state can be understood as a sum over pure states, weighted by classical probabilities ; likewise, the Bures metric is a weighted sum of the Fubini–Study metric. For a time-varying Hamiltonian H t and time-varying density matrix ρ ρ t , the variance of the energy is given by