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Rubinow, S. I.

 
9781333244804: Effective Two-Body Method for Two-Electron Atoms (Classic Reprint)

Sinopsis

A practical approach to simplify the two-electron atom problem that still yields reliable results. This book explains how a three-body quantum system can be treated as an effective two-body problem. By focusing on a single variable and using a variational principle, it offers a clear path to approximate ground-state energies, with results that closely match known values for helium-like atoms.

In this edition, the method is developed from classic ideas and extended with a flexible parameter to improve accuracy. It shows how the effective two-body wave function can resemble hydrogenic solutions and how bounds on energies emerge from variational reasoning. The discussion also covers potential refinements and why this approach can be a useful stepping stone for more complex calculations.


  • How the three-body problem is reduced to an effective two-body form.

  • Hydrogenic-like solutions and the role of a variational parameter.

  • How energy bounds are obtained and why results stay close to experimental values.

  • Ideas for refining the method and exploring future improvements.



Ideal for readers of theoretical atomic physics, and for anyone exploring practical variational methods in quantum mechanics.

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Reseña del editor

Excerpt from Effective Two-Body Method for Two-Electron Atoms

In the present note we wish to present some Observations on the non relativistic two-electron atomic system. We hope these may prove useful and stimulating to additional efforts to Obtain approximate eigenfunctions and eigenvalues. In particular, we examine the reduction of the problem.to an effective two-body' system, an idea that has been used in the corresponding three-bodyr nuclear system, the triton [l] [2] A complete review of the extensive treatment of the two-electron atomic system, in particular the helium atom, may be found in the recent book of Bethe and Salpeter[5]. The variational formulation of the problem, which is the basis of the present investigation, is reviewed here.

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