Rayleigh-Schrodinger perturbation theory with a strong perturbation

Anharmonic oscillators

M. Cohen, S. Kais

Research output: Contribution to journalArticle

10 Citations (Scopus)

Abstract

The bound state solutions of Schrodinger's equation for the anharmonic oscillator potentials V=x2+ lambda x2k (k=2,3, . . . ) have been investigated, using elementary techniques of low-order variational perturbation theory. For the quartic oscillator (k=2) a scaled harmonic potential provides a remarkably accurate model for all lambda . Although this model is slightly less satisfactory for higher-order anharmonicities (k>or=3), the perturbation procedures remain effective, and can be applied successfully provided that higher-order terms are calculated.

Original languageEnglish
Article number021
Pages (from-to)683-690
Number of pages8
JournalJournal of Physics A: Mathematical and General
Volume19
Issue number5
DOIs
Publication statusPublished - 1 Dec 1986
Externally publishedYes

Fingerprint

Anharmonic Oscillator
Rayleigh
Perturbation Theory
perturbation theory
oscillators
Higher Order
Schrodinger equation
Perturbation
perturbation
Harmonic Potential
Schrodinger Equation
Quartic
Bound States
harmonics
Term
Model

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Physics and Astronomy(all)
  • Mathematical Physics

Cite this

Rayleigh-Schrodinger perturbation theory with a strong perturbation : Anharmonic oscillators. / Cohen, M.; Kais, S.

In: Journal of Physics A: Mathematical and General, Vol. 19, No. 5, 021, 01.12.1986, p. 683-690.

Research output: Contribution to journalArticle

@article{eb77a21ea58e4b419d5a5f4926c5962c,
title = "Rayleigh-Schrodinger perturbation theory with a strong perturbation: Anharmonic oscillators",
abstract = "The bound state solutions of Schrodinger's equation for the anharmonic oscillator potentials V=x2+ lambda x2k (k=2,3, . . . ) have been investigated, using elementary techniques of low-order variational perturbation theory. For the quartic oscillator (k=2) a scaled harmonic potential provides a remarkably accurate model for all lambda . Although this model is slightly less satisfactory for higher-order anharmonicities (k>or=3), the perturbation procedures remain effective, and can be applied successfully provided that higher-order terms are calculated.",
author = "M. Cohen and S. Kais",
year = "1986",
month = "12",
day = "1",
doi = "10.1088/0305-4470/19/5/021",
language = "English",
volume = "19",
pages = "683--690",
journal = "Journal of Physics A: Mathematical and Theoretical",
issn = "1751-8113",
publisher = "IOP Publishing Ltd.",
number = "5",

}

TY - JOUR

T1 - Rayleigh-Schrodinger perturbation theory with a strong perturbation

T2 - Anharmonic oscillators

AU - Cohen, M.

AU - Kais, S.

PY - 1986/12/1

Y1 - 1986/12/1

N2 - The bound state solutions of Schrodinger's equation for the anharmonic oscillator potentials V=x2+ lambda x2k (k=2,3, . . . ) have been investigated, using elementary techniques of low-order variational perturbation theory. For the quartic oscillator (k=2) a scaled harmonic potential provides a remarkably accurate model for all lambda . Although this model is slightly less satisfactory for higher-order anharmonicities (k>or=3), the perturbation procedures remain effective, and can be applied successfully provided that higher-order terms are calculated.

AB - The bound state solutions of Schrodinger's equation for the anharmonic oscillator potentials V=x2+ lambda x2k (k=2,3, . . . ) have been investigated, using elementary techniques of low-order variational perturbation theory. For the quartic oscillator (k=2) a scaled harmonic potential provides a remarkably accurate model for all lambda . Although this model is slightly less satisfactory for higher-order anharmonicities (k>or=3), the perturbation procedures remain effective, and can be applied successfully provided that higher-order terms are calculated.

UR - http://www.scopus.com/inward/record.url?scp=3042987649&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=3042987649&partnerID=8YFLogxK

U2 - 10.1088/0305-4470/19/5/021

DO - 10.1088/0305-4470/19/5/021

M3 - Article

VL - 19

SP - 683

EP - 690

JO - Journal of Physics A: Mathematical and Theoretical

JF - Journal of Physics A: Mathematical and Theoretical

SN - 1751-8113

IS - 5

M1 - 021

ER -