Summation of asymptotic expansions of multiple-valued functions using algebraic approximants: application to anharmonic oscillators
نویسندگان
چکیده
The divergent Rayleigh-Schrr odinger perturbation expansions for energy eigenvalues of cubic, quartic, sextic and octic oscillators are summed using algebraic approximants. These approximants are generalized Pad e approximants that are obtained from an algebraic equation of arbitrary degree. Numerical results indicate that given enough terms in the asymptotic expansion the rate of convergence of the diagonal staircase approximant sequence increases with the degree. Diierent branches of the approximants converge to diierent branches of the function. The success of the high-degree approximants is attributed to their ability to model the function on multiple sheets of the Riemann surface and to reproduce the correct singularity structure in the limit of large perturbation parameter. An eecient recursive algorithm for computing the diagonal approximant sequence is presented.
منابع مشابه
Convergent Rayleigh–Schrödinger perturbation expansions for low-lying eigenstates and eigenenergies of anharmonic oscillators in intermediate basis states
With suitably chosen unperturbed Hamiltonians, we show numerical evidence of convergence of Rayleigh–Schrödinger perturbation expansions for low-lying eigenstates and the corresponding eigenenergies of the quartic, sextic, and octic anharmonic oscillators, when the anharmonic terms are not very strong. In obtaining the perturbation expansions, unperturbed Hamiltonians are taken as the diagonal ...
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