We investigate the convergence properties of a perturbation method proposed some time ago and reveal some of its most interesting features. Anharmonic oscillators in the strong-coupling limit prove to be appropriate illustrative examples and a suitable benchmark.
We investigate the perturbative expansions of the ground-state wavefunctions of the quantum anharmonic oscillators. With an appropriate change of spatial scale, the weak-coupling Schrödinger equation is transformed to an equivalent strong-coupling one. The Friedberg–Lee–Zhao method is applied to obtain the improved perturbative expansions. These perturbative expansions give a correction to the WKB results for large spatial distances, and reproduce the conventional weak-coupling results for small spatial distances.