Note that in the expression of density above, the summation is over all N b Kohn–Sham orbitals and f j ( t ) is the time-dependent occupation number for orbital j . If the potential v s (r, t) can be determined, or at the least well-approximated, then the original Schrödinger equation, a single partial differential equation in 3 N variables, has been replaced by N differential equations in 3 dimensions, each differing only in the initial condition.