## Abstract

We show that the method of self-similar approximations, suggested recently by one of the authors, can be successfully applied to the eigenvalue problem. This method makes it possible to find an effective sum of a divergent series by using only a few terms of perturbation theory. As an illustration, we calculate eigenvalues for the anharmonic-oscillator Hamiltonian. We demonstrate that invoking only two first terms of perturbation theory we are able to reconstruct the whole spectrum of the anharmonic oscillator with an accuracy not worse than of the order of 10{sup -3} for any energy level and all anharmonicity constants. 10 refs.

## Citation Formats

Kadantseva, E P, and Yukalov, V I.
Self-similar approximations for eigenvalue problem.
JINR: N. p.,
1991.
Web.

Kadantseva, E P, & Yukalov, V I.
Self-similar approximations for eigenvalue problem.
JINR.

Kadantseva, E P, and Yukalov, V I.
1991.
"Self-similar approximations for eigenvalue problem."
JINR.

@misc{etde_10119421,

title = {Self-similar approximations for eigenvalue problem}

author = {Kadantseva, E P, and Yukalov, V I}

abstractNote = {We show that the method of self-similar approximations, suggested recently by one of the authors, can be successfully applied to the eigenvalue problem. This method makes it possible to find an effective sum of a divergent series by using only a few terms of perturbation theory. As an illustration, we calculate eigenvalues for the anharmonic-oscillator Hamiltonian. We demonstrate that invoking only two first terms of perturbation theory we are able to reconstruct the whole spectrum of the anharmonic oscillator with an accuracy not worse than of the order of 10{sup -3} for any energy level and all anharmonicity constants. 10 refs.}

place = {JINR}

year = {1991}

month = {Dec}

}

title = {Self-similar approximations for eigenvalue problem}

author = {Kadantseva, E P, and Yukalov, V I}

abstractNote = {We show that the method of self-similar approximations, suggested recently by one of the authors, can be successfully applied to the eigenvalue problem. This method makes it possible to find an effective sum of a divergent series by using only a few terms of perturbation theory. As an illustration, we calculate eigenvalues for the anharmonic-oscillator Hamiltonian. We demonstrate that invoking only two first terms of perturbation theory we are able to reconstruct the whole spectrum of the anharmonic oscillator with an accuracy not worse than of the order of 10{sup -3} for any energy level and all anharmonicity constants. 10 refs.}

place = {JINR}

year = {1991}

month = {Dec}

}