Anharmonic oscillator analysis using modified Airy functions

We have applied the modified Airy function (MAF) method to the analysis of an anharmonic oscillator, characterized by the potential V(x) = k x2/2 + a x4, k > 0, a > 0. The MAF method gives an accurate closed-form expression for the wave function as well as very accurate eigenvalues with much less numerical effort than the five-term (eighth-order) WKBJ approximation. The application of the first-order perturbation correction to the MAF eigenvalues makes them even more accurate than those obtained by the five-term WKBJ approximation.