Convergence of scaled delta expansion: Anharmonic oscillator

We prove that the linear delta expansion for energy eigenvalues of the quantum mechanical anharmonic oscillator converges to the exact answer if the order dependent trial frequency Ω is chosen to scale with the order as Ω=CNγ; 1/3<γ<1/2, C>0 as N → ∞. It converges also for γ=1/3, if C≥αc g1/3, αc congruent 0.570875, where g is the coupling constant in front of the operator q4/4. The extreme case with γ=1/3, C=αc g1/3 corresponds to the choice discussed earlier by Seznec and Zinn-Justin and, more recently, by Duncan and Jones. copyright 1995 Academic Press, Inc