Springer Online Journal Archives 1860-2000
Abstract A matrix moment problem is considered in connection with anyx 2m (m=2, 3, 4, ...) anharmonic oscillator as well as the (:φ2m (x):g(x))2 (m=2, 3) field theory models, whose Rayleigh-Schrödinger perturbation expansions for the ground state eigenvalue are known to diverge. The approximants related to such a problem are proven to converge to the eigenvalue, when applied to an expansion of the Brillouin-Wigner type. These approximants, whose construction involves only matrix elements occurring in the Rayleigh-Schrödinger expansion, are the approximants of aJ-type matrix continued fraction, i.e. the [N−1,N] matrix Padé approximants. The explicit analytical expression of matrix continued fraction is found in the anharmonic oscillators case.
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