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Il Nuovo Cimento A (1965-1970)

, Volume 50, Issue 2, pp 333–338 | Cite as

Separability of schrödinger and Klein-Gordon equations with a vector potential

  • A. C. T. Wu
Article

Summary

Necessary and sufficient conditions are given for separability of the Schrödinger equation with a vector potential. The physical meaning of the condition on the vector potential is visualized with the aid of gauge invariance. The analysis can be carried out formally for the Klein-Gordon case.

Keywords

Scalar Potential Gauge Invariance Zione Schr6dinger Equation Separable Solution 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Разделение уравнений Шредингера и Клейна-Гордона с векторным потенциалом

Резюме

Приводятся необходимые и достаточные условия для разделения уравнения Шрединтера с векторным потенциалом. С помощью калибровочной инвариантности устанавливается физический смысл условия на векторные потенциалы. Формально анализ может быть проведен и для случая Клейна-Гордона.

Riassunto

Si danno le condizioni necessarie e sufficienti per la separabilità dell'equazione di Schrödinger con un potenziale vettoriale. Si visualizza il significato fisico della condizione per il potenziale con l'aiuto dell'invarianza di gauge. Si può eseguire formalmente l'analisi nel caso di Klein-Gordon.

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References

  1. (1).
    P. G. Stäckel:Über die Integration der Hamilton-Jacobischen Differential-gleichung mittels Separation der Variablen (Habilitationsschrift, Halle, 1891);Math. Ann.,49, 145 (1897).Google Scholar
  2. (2).
    H. P. Robertson:Math. Ann.,98, 749 (1927).CrossRefGoogle Scholar
  3. (3).
    L. P. Eisenhart:Ann. Math.,35, 284 (1934).MathSciNetCrossRefGoogle Scholar
  4. (4).
    L. P. Eisenhart:Phys. Rev.,74, 87 (1948).ADSMathSciNetCrossRefGoogle Scholar
  5. (5).
    For discussion on the separability on Helmholtz and Laplace equations, see,e.g.,P. Moon andD. E. Spencer:Journ. Franklin Inst.,253, 585 (1952).MathSciNetCrossRefGoogle Scholar
  6. (6).
    An elementary exposition on the separable co-ordinates may be found inP. M. Morse andH. Feshbach:Methods of Theoretical Physics, Part I, Scet.5.1 (New York, 1953).Google Scholar

Copyright information

© Società Italiana di Fisica 1967

Authors and Affiliations

  • A. C. T. Wu
    • 1
  1. 1.Department of PhysicsUniversity of MichiganAnn Arbor

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