This equation can be rewritten as a system of differential equations specifying the time evolution of the coefficients a n ( t ) : i ℏ ℏ d a k ( t ) d t = ∑ ∑ n ⟨ ⟨ k | H ′ | n ⟩ ⟩ a n ( t ) e i t ( E k − − E n ) / ℏ ℏ . This equation is exact, but normally cannot be solved in practice.