Energy levels of the quartic double well using a phase-integral method

Approximate energy eigenvalues for the double-well quartic oscillator are calculated using the phase-integral method of Froman and Froman up to the fifth-order approximation. By means of appropriate transformations, the integrals appearing in the quantization condition are expressed in terms of integrals solved in previous papers. Different approximations are discussed. In general, the results are very good