Rayleigh-Schrodinger perturbation theory with a strong perturbation: Anharmonic oscillators

The bound state solutions of Schrodinger's equation for the anharmonic oscillator potentials V=x²+ lambda x^2k (k=2,3, . . . ) have been investigated, using elementary techniques of low-order variational perturbation theory. For the quartic oscillator (k=2) a scaled harmonic potential provides a remarkably accurate model for all lambda . Although this model is slightly less satisfactory for higher-order anharmonicities (k>or=3), the perturbation procedures remain effective, and can be applied successfully provided that higher-order terms are calculated.