Abstract The accurate eigenfunctions of first order in λ of a double-well oscillator by means of power series expansion of the solution of the Schrödinger equation of double-well anharmonic potential are calculated. To check the accuracy of the calculated eigenfunctions, we compared them to those obtained by a perturbation approach. It is shown that our results are the same as those derived by the perturbation method. Using the Riccati–Padé method some eigenvalues of the anharmonic potential are also calculated
