The Rayleigh-Schrodinger perturbation series for the cubic anharmonic oscillator can be formally rearranged as the classical Birkhoff series plus quantum corrections proportional to successive powers of h(cross) 2 . Each of the individual quantum corrections is a convergent power series expansion (with the same radius of convergence as the classical series) of the corresponding term in the Jeffreys-Wentzel-Kramers-Brillouin series.
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Gabriel Álvarez (1989) studied this question.
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