where ν (h, F) is a correction factor that in general has to be found by numerical integration. For the special case of a Schottky–Nordheim barrier, an analytical result exists and ν (h, F) is given by ν (f h), as discussed above; approximation (11) for ν (f h) is more than sufficient for all technological purposes. The pre-factor P is also in principle a function of h and (maybe) F, but for the simple physical models discussed here it is usually satisfactory to make the approximation P = 1. The exact triangular barrier is a special case where the Schrödinger equation can be solved exactly, as was done by Fowler and Nordheim; for this physically unrealistic case, ν (f h) = 1, and an analytical approximation for P exists.