Comment on "Freeman Dyson was right about analyticity and perturbation series"

Abstract

In this comment we analyze the results derived recently by Bowen et al (2014 Phys. Scr. 89 015301). We first show that the eigenvalues of the family of the anharmonic oscillators studied by those authors already exhibit a branch point but it is irrelevant for perturbation theory. Second, we show that one of the authors' main contributions, namely that the variational method yields the correct dependence of the eigenvalues on the coupling constant, has been known since long ago. Third, the authors' statement that their Bohr–Sommerfeld eigenvalues are exact is proved wrong by comparison with accurate numerical results.