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Self-similar approximations for eigenvalue problem

Technical Report:

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.
Publication Date:
Dec 31, 1991
Product Type:
Technical Report
Report Number:
JINR-E-5-91-466
Reference Number:
SCA: 661100; PA: AIX-24:008096; SN: 93000932837
Resource Relation:
Other Information: DN: Submitted to Comput. Phys.; PBD: 1991
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; EIGENVALUES; ANHARMONIC OSCILLATORS; PERTURBATION THEORY; ACCURACY; CONVERGENCE; DISTRIBUTION FUNCTIONS; HAMILTONIANS; ONE-DIMENSIONAL CALCULATIONS; RENORMALIZATION; WKB APPROXIMATION; 661100; CLASSICAL AND QUANTUM MECHANICS
OSTI ID:
10119421
Research Organizations:
Joint Inst. for Nuclear Research, Dubna (Russian Federation). Lab. of Theoretical Physics
Country of Origin:
JINR
Language:
English
Other Identifying Numbers:
Other: ON: DE93612978; TRN: RU9206939008096
Availability:
OSTI; NTIS (US Sales Only); INIS
Submitting Site:
INIS
Size:
[15] p.
Announcement Date:
Jun 30, 2005

Technical Report:

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}
}