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

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

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