Rayleigh-Schroedinger perturbation theory with a strong perturbation: anharmonic oscillators

The bound state solutions of Schrodinger's equation for the anharmonic oscillator potentials V = x2 + lambdaxsup(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 >=3), the present perturbation procedures remain effective, and can be applied successfully provided that higher-order terms are calculated. (authors)