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Algebraic treatment of the Stark effect for hydrogen

Алгебраическое расс мотрение Штарк-эффек та для водорода

  • Published:
Il Nuovo Cimento B (1971-1996)

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Summary

The Stark effect for the hydrogen atom is treated in the context of the Majorana-type, infinite-component equation, proposed by Fronsdal. A convenient perturbative method is developed and the Stark effect calculated up to the second order for any level and up to the fourth order for the ground state. The perturbative method illustrated here may be of interest for dealing with other infinite-component equations, containing small terms, nonlinear in theSO 4,2 generators, which are not amenable to an exact treatment.

Riassunto

Si tratta l’effetto Stark per l’atomo di idrogeno nel oontesto dell’equazione ad infinite componenti, del tipo di Majorana, proposta da Fronsdal. Si sviluppa un opportuno metodo perturbativo e si calcola l’effetto Stark fino al secondo ordine per un qualunque livello e fino al quarto ordine per lo stato fondamentale. Il metodo perturbativo descritto in questo artioolo può essere utile nella trattazione di altre equazioni ad infinite componenti, contenenti termini piccoli non lineari nei generatori diSO 4,2, che non sono riconducibili ad una trattazione esatta.

Резюме

Рассматривается Шта рк-эффект для водород а в связи с бесконечно компонентным уравне нием типа Майорана, ко торое было предложено Фронсдал ом. Развивается удобный пертурбационный мет од и вычисляется Штарк-эф фект до второго порядка для л юбого уровня и до четв ертого порядка для основног о состояния. Рассмотренный здесь пертурбационный мет од может быть интересен при исслед овании других уравнений с бе сконечным числом ком понент, которые содержат малые члены, нелинейн ые относительно гене раторов SO4,2, которые не могут быть рассмотрены точно.

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References

  1. C. Fronsdal:Phys. Rev.,156, 1665 (1967).

    Article  ADS  Google Scholar 

  2. E. Majorana:Nuovo Cimento,9, 335 (1932).

    Article  Google Scholar 

  3. A. O. Barut andH. Kleinert:Phys. Rev.,156, 1541 (1967);157, 1180 (1967).

    Article  ADS  Google Scholar 

  4. H. Kleinert:Forstsch. Phys.,16, 1 (1968).

    Article  Google Scholar 

  5. C. Fronsdal: ICTP, Trieste, preprint IC/68/85.

  6. C. Fronsdal andL. E. Lundberg: ICTP, Trieste, IC/69/33.

  7. A. O. Barut:Lectures at the Theoretical Physics Institute, University of Colorado, Summer 1967.

  8. L. Landau andE. Lifchitz:Mécanique quantique (Moscow, 1966), p.319.

  9. A. Dalgarno: inQuantum Theory, edited byD. E. Bates, vol.1 (New York, 1961), p.171.

  10. C. Fronsdal:Phys. Rev.,171, 1811 (1968).

    Article  ADS  Google Scholar 

  11. J. D. Bekenstein andJ. B. Krieger:Phys. Rev.,188, 130 (1969).

    Article  MathSciNet  ADS  Google Scholar 

  12. Y. Nambu: inSymmetry principles at high, energy, Coral Gables Conference (San Francisco, 1967), p. 62.

  13. P. Leal Ferreira:Rev. Mex. Phys.,18, 233 (1969).

    Google Scholar 

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Authors and Affiliations

  1. Istituto de Fisica Teórica-São Paulo, Brasil

    A. Romero Lopes & P. Leal Ferreira

Authors
  1. A. Romero Lopes
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  2. P. Leal Ferreira
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Additional information

To speed up publication, the authors of this paper have agreed to not receive the proofs for correction.

Work supported in part by the Banco Nacional do Desenvolvimento Econômico, FUNTEC, Brazil.

With a fellowship from the Conselho Nacional de Pesquisas, Brazil.

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Lopes, A.R., Ferreira, P.L. Algebraic treatment of the Stark effect for hydrogen. Nuov Cim B 3, 23–33 (1971). https://doi.org/10.1007/BF02899938

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  • DOI: https://doi.org/10.1007/BF02899938

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