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 = CN ; 1/3 < γ < 1/2, C > 0 as N → ∞. It converges also for γ = 1/3, if C ≥ αcg, αc ≃ 0.570875, where g is the coupling constant in front of the operator q/4. The extreme case with γ = 1/3, C = αcg 1/3 corresponds to the choice discussed earlier by Seznec and Zinn-Justin and, more recently, by Duncan and Jones. GEF-Th-7/1994 July 1994 † Address for September 1994–June 1995: Univ. de Paris, Centre d’Orsay, France. ∗ On leave of absence from Department of Physics, Ibaraki University, Mito 310, Japan (address after 1 September 1994).