### Abstract

The bound state solutions of Schrodinger's equation for the anharmonic oscillator potentials V=x^{2}+ lambda x^{2k} (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 language | English |
---|---|

Article number | 021 |

Pages (from-to) | 683-690 |

Number of pages | 8 |

Journal | Journal of Physics A: Mathematical and General |

Volume | 19 |

Issue number | 5 |

DOIs | |

Publication status | Published - 1 Dec 1986 |

Externally published | Yes |

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### 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.

Research output: Contribution to journal › Article

*Journal of Physics A: Mathematical and General*, vol. 19, no. 5, 021, pp. 683-690. https://doi.org/10.1088/0305-4470/19/5/021

}

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 -