### Abstract

The variational principle for eigenvalue problems with a nonidentity weight operator is used to establish upper or lower bounds on critical parameters of quantum systems. Three problems from atomic physics are considered as examples. Critical screening parameters for the exponentially screened Coulomb potential are found using a trial function with one nonlinear variational parameter. The critical charge for the helium isoelectronic series is found using a Hylleraas-type trial function. Finally, critical charges for the same system subjected to a magnetic field are found using a product of two hydrogen-like basis sets.

Original language | English |
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Pages (from-to) | 6891-6896 |

Number of pages | 6 |

Journal | Journal of Physics A: Mathematical and General |

Volume | 32 |

Issue number | 39 |

DOIs | |

Publication status | Published - 1 Oct 1999 |

Externally published | Yes |

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### ASJC Scopus subject areas

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

### Cite this

*Journal of Physics A: Mathematical and General*,

*32*(39), 6891-6896. https://doi.org/10.1088/0305-4470/32/39/312

**Variational principle for critical parameters of quantum systems.** / Sergeev, A. V.; Kais, S.

Research output: Contribution to journal › Article

*Journal of Physics A: Mathematical and General*, vol. 32, no. 39, pp. 6891-6896. https://doi.org/10.1088/0305-4470/32/39/312

}

TY - JOUR

T1 - Variational principle for critical parameters of quantum systems

AU - Sergeev, A. V.

AU - Kais, S.

PY - 1999/10/1

Y1 - 1999/10/1

N2 - The variational principle for eigenvalue problems with a nonidentity weight operator is used to establish upper or lower bounds on critical parameters of quantum systems. Three problems from atomic physics are considered as examples. Critical screening parameters for the exponentially screened Coulomb potential are found using a trial function with one nonlinear variational parameter. The critical charge for the helium isoelectronic series is found using a Hylleraas-type trial function. Finally, critical charges for the same system subjected to a magnetic field are found using a product of two hydrogen-like basis sets.

AB - The variational principle for eigenvalue problems with a nonidentity weight operator is used to establish upper or lower bounds on critical parameters of quantum systems. Three problems from atomic physics are considered as examples. Critical screening parameters for the exponentially screened Coulomb potential are found using a trial function with one nonlinear variational parameter. The critical charge for the helium isoelectronic series is found using a Hylleraas-type trial function. Finally, critical charges for the same system subjected to a magnetic field are found using a product of two hydrogen-like basis sets.

UR - http://www.scopus.com/inward/record.url?scp=0033208843&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0033208843&partnerID=8YFLogxK

U2 - 10.1088/0305-4470/32/39/312

DO - 10.1088/0305-4470/32/39/312

M3 - Article

VL - 32

SP - 6891

EP - 6896

JO - Journal of Physics A: Mathematical and Theoretical

JF - Journal of Physics A: Mathematical and Theoretical

SN - 1751-8113

IS - 39

ER -