Are atomic Hartree-Fock equations linearizable?

  • Carl E. Wulfman
Session II — Completely Integrable Systems and Group Theory
Part of the Lecture Notes in Physics book series (LNP, volume 180)


No generator Lo is of the required form. Therefore we have definitively established that the H-F equations (1) are not linearizable by a 1:1 transformation of the space of variables≠, ψ, ψ*, ϕ, Z = ζ-ε · 21/2r, when \(\psi (\vec r)\) is invariant under rotations.

We wish to thank Sukeyuki Kumei for an early communication, and helpful discussion, of the linearization analysis he and George Bluman discovered.


Differential Equa Tions State Quantum Mechanic Early Communication Schroedinger Equation Fixed Core 
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  1. 1.
    S. Kumei G.W. Bluman, Siam J, Appl. Math,, in press.Google Scholar
  2. 2.
    For a discussion of these methods, examples of their application and further references, c.f.Google Scholar
  3. 2.a)
    C.E. Wulfman, “Dynamical Groups in Atomic and Molecular Physics”, in “Recent Advances in Group Theory and their application to Spectroscopy”, J.C, Donini, ed. (Plenum, N.Y., 1979).Google Scholar
  4. 2.b)
    G.W. Bluman, J. Cole, “Similarity Methods for Differential Equations“ (Springer, N.Y., 1974).Google Scholar
  5. 2.c)
    C.E. Wulfman, “Systematic Methods for Determining the Lie Groups Admitted by Differential Equations”, in “Symmetries in Science”, B. Gruber, R.S. Millmann, eds. (Plenum, N.Y., 1980).Google Scholar

Copyright information

© Springer-Verlag 1983

Authors and Affiliations

  • Carl E. Wulfman
    • 1
  1. 1.Department of PhysicsUniversity of The PacificStockton

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