An asymptotic expansion for energy eigenvalues of anharmonic oscillators

In the present contribution, we derive an asymptotic expansion for the energy eigenvalues of anharmonic oscillators for potentials of the form V(x)=κx2q+ωx2,q=2,3,… as the energy level n approaches infinity. The asymptotic expansion is obtained using the WKB theory and series reversion. Furthermore, we construct an algorithm for computing the coefficients of the asymptotic expansion for quartic anharmonic oscillators, leading to an efficient and accurate computation of the energy values for n≥6. •We derived the asymptotic expansion for energy eigenvalues of anharmonic oscillators.•A highly efficient recursive algorithm for computing Sk′(z) for WKB.•We contributed to series reversion theory by reverting a new form of asymptotic series.•Our numerical algorithm achieves high accuracy for higher energy levels.