### Abstract

It is shown by use of the variation theorem, that under fairly general conditions the energy given to an odd order of approximation by perturbation theory is an upper bound to the correct energy. Under less general conditions it is shown that for a positive definite perturbation the energy given by an even-order approximation is a lower bound and for a negative definitive perturbation it is again an upper bound. Some applications are discussed.

Language | English |
---|---|

Pages | 276-277 |

Number of pages | 2 |

Journal | The Journal of Chemical Physics |

Volume | 29 |

Issue number | 2 |

Publication status | Published - 1958 |

Externally published | Yes |

### Fingerprint

### Cite this

*The Journal of Chemical Physics*,

*29*(2), 276-277.

}

*The Journal of Chemical Physics*, vol. 29, no. 2, pp. 276-277.

**Application of schwarz's inequality to perturbation theory.** / Gray, B. F.

Research output: Contribution to journal › Article › Research › peer-review

TY - JOUR

T1 - Application of schwarz's inequality to perturbation theory

AU - Gray, B. F.

PY - 1958

Y1 - 1958

N2 - It is shown by use of the variation theorem, that under fairly general conditions the energy given to an odd order of approximation by perturbation theory is an upper bound to the correct energy. Under less general conditions it is shown that for a positive definite perturbation the energy given by an even-order approximation is a lower bound and for a negative definitive perturbation it is again an upper bound. Some applications are discussed.

AB - It is shown by use of the variation theorem, that under fairly general conditions the energy given to an odd order of approximation by perturbation theory is an upper bound to the correct energy. Under less general conditions it is shown that for a positive definite perturbation the energy given by an even-order approximation is a lower bound and for a negative definitive perturbation it is again an upper bound. Some applications are discussed.

UR - http://www.scopus.com/inward/record.url?scp=36849140822&partnerID=8YFLogxK

M3 - Article

VL - 29

SP - 276

EP - 277

JO - The Journal of Chemical Physics

T2 - The Journal of Chemical Physics

JF - The Journal of Chemical Physics

SN - 0021-9606

IS - 2

ER -