Convergence of the Optimized Delta Expansion for the Connected Vacuum Amplitude -- Anharmonic Oscillator

Abstract

The convergence of the linear $\delta$ expansion for the connected generating functional of the quantum anharmonic oscillator is proved. Using an order-dependent scaling for the variational parameter $\lambda$, we show that the expansion converges to the exact result with an error proportional to $\exp (-c{N}^{1/3})$.

LaTeX, 14 pages, 4 figures.