SCALING PROPERTY OF VARIATIONAL PERTURBATION EXPANSION FOR A GENERAL ANHARMONIC-OSCILLATOR WITH X(P)-POTENTIAL

We prove a powerful scaling property for the extremality condition in the recently developed variational perturbation theory which converts divergent perturbation expansions into exponentially fast convergent ones. The proof is given for the energy eigenvalues of an anharmonic oscillator with an arbitrary x(p)-potential. The scaling property greatly increases the accuracy of the results.