Anharmonic Oscillator

Abstract

We solve the anharmonic-oscillator problem as given by Bender and Wu to include the ${\ensuremath{\hbar}}^{4}$ terms for the energy eignevalues and the ${\ensuremath{\hbar}}^{2}$ 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.