Calculation of eigenfunctions in a double-well oscillator

The accurate eigenfunctions of first order in lambda of a double-well oscillator by means of power series expansion of the solution of the Schrodinger 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-Pade method some eigenvalues of the anharmonic potential are also calculated.