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A method for summing strongly divergent perturbation series: The Zeeman effect in hydrogen

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  • Artega, Gustavo A.
  • Fernández, Francisco M.
  • Mesón, Alejandro M.
  • Castro, Eduardo A.

Abstract

A new method for summing strongly divergent power series is presented. It consists of an order-dependent mapping that transforms the divergent series into a convergent sequence. The procedure is applied to the perturbation series of the Zeeman effect in hydrogen obtaining accurate energy values for the states 1s and 2p±1 over a wide range of field strengths. Difficulties in handling the 2s state are pointed out.

Suggested Citation

  • Artega, Gustavo A. & Fernández, Francisco M. & Mesón, Alejandro M. & Castro, Eduardo A., 1984. "A method for summing strongly divergent perturbation series: The Zeeman effect in hydrogen," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 128(1), pages 253-267.
    • Handle: RePEc:eee:phsmap:v:128:y:1984:i:1:p:253-267
    DOI: 10.1016/0378-4371(84)90090-6
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    1. Zinnes, Dina A., 1979. "War and Domestic Political Violence: The American Capacity for Repression and Reaction. By Michael Stohl. (Beverly Hills, Calif.: Sage Publications, 1976. Pp. 153. $14.00, cloth; $6.95, paper.)," American Political Science Review, Cambridge University Press, vol. 73(3), pages 954-955, September.
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    1. Arteca, Gustavo A. & Fernández, Francisco M. & Castro, Eduardo A., 1984. "A method for summation of perturbation series," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 128(3), pages 589-610.

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