Asymptotic Perturbation Theory — Anharmonic Oscillator H = p²/2 + x²/2 + λx⁴

Bender–Wu (1969): the perturbation series diverges for every λ > 0 (Dyson argument). Yet the partial sums are asymptotically useful: error first decreases, reaches a minimum at N_opt ≈ 1/(2λ), then grows without bound. Exact energies via finite-difference matrix diagonalization (shift-invert iteration).