When a thermodynamic quantum system is at equilibrium there is no definite phase relationship between the energy eigenstates of the system. The system is in a mixed state, and the probability of any measured value of any quantity is independent of time because the phases of the energy components of the system cannot interfere. In the case of an isolated quantum system, however, the state may be represented by a pure state (taken at time zero, say), 
, with the sum of the component amplitudes being one, 
, and the 
are taken as energy eigenstates. The time evolution of such a state is simple, with each energy component being multiplied by 
following immediately from the Schrodinger equation, equation 7.1. Thus, the time evolution of the state 
above is given by
and the probability of finding the system in the state 
at time t is given by
Clearly this is not independent of time because the second term is time dependent, unless is itself an energy eigenstate, or unless all of the energy eigenstates with nonzero amplitude are degenerate - having the same energy.