Abstract
No generator L o 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.
Research supported by NSF Grant CHE 8014165.
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References
S. Kumei G.W. Bluman, Siam J, Appl. Math,, in press.
For a discussion of these methods, examples of their application and further references, c.f.
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).
G.W. Bluman, J. Cole, “Similarity Methods for Differential Equations“ (Springer, N.Y., 1974).
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).
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© 1983 Springer-Verlag
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Wulfman, C.E. (1983). Are atomic Hartree-Fock equations linearizable?. In: Serdaroğlu, M., Ínönü, E. (eds) Group Theoretical Methods in Physics. Lecture Notes in Physics, vol 180. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-12291-5_26
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DOI: https://doi.org/10.1007/3-540-12291-5_26
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