Anharmonic Oscillator

We solve the anharmonic-oscillator problem as given by Bender and Wu to include the ${\hslash }^4$ terms for the energy eignevalues and the ${\hslash }^2$ terms for the eigenfunctions by means of the Miller and Good modified WKB method. This is done by accepting the harmonic oscillator as a solved problem. We see that in doing so, not only can we get better energy eigenvalues, but also we can get improved eigenfunctions.