Abstract
In previous lectures, I have discussed how one can extract from QED an effective relativistic hamiltonian and shown how this can be expressed in terms of Slater integrals involving only radial functions defined in terms of a suitable one-body potential. From this point on, the process is very close to that employed in non-relativistic calculations of similar type.
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References
J.K.L. MacDonald, Phys. Rev. 43: 830 (1933); the theorem, in a different guise is familiar to numerical analysts, e.g. A. Ralston,“A first course in numerical analysis”, Theorem 10.15, page 495. McGraw Hill, New York (1965).
See, for example, articles in Proceedings of Nobel Symposium 46; Phys. Scripta, 21, nos. 3–4 (1980).
D.P. Carroll, H.J. Silverston and R.M. Metzger, J. Chem. Phys. 71: 4142 (1979).
W. Eissner, M. Jones, H. Nussbaumer, Computer Phys. Commun. 8: 270 (1974); M. Klapisch, ibid, 2: 239 (1971); M. Klapisch, J.L. Schwöb, B,S. Fraenkel and J. Oreg, J. Opt. Soc. Amer 67: 148 (1977); and subsequent papers.
I.P. Grant, these proceedings; we use here the notation of I.P. Grant, B.J. McKenzie, P.H. Norrington, D.F. Mayers and N.C. Pyper, Computer Phys. Commun. 21: 207 (1980).
I.P. Grant, D.F. Mayers and N.C. Pyper, J. Phys. B. 9: 2777 (1976).
J. Hata and I.P. Grant, J. Phys. B. 14: 2111 (1981).
K.K. Docken and J. Hinze, J. Chem. Phys. 57: 4928 (1972).
I.P. Grant, Adv. Phys. 19: 747 (1970).
I.P. Grant, these proceedings.
I.P. Grant, Phys. Scripta, 21: 443 (1980).
G.L. Malli and J. Oreg, J. Chem. Phys. 63: 830 (1975); J. Oreg and G.L. Malli, ibid, 65: 1746, 1755 (1976); 0. Matsuoka, N. Suzuki, T. Aoyama and G.L. Malli, ibid, 73: 1320, 1329 (1980); J.C. Barthelat, M. Pelissier and Ph. Durand, Phys. Rev. A21: 1773 (1980): G.L. Malli, these proceedings, and many others.
F. Mark, H. Lischka and F. Rosicky, Chem. Phys. Letts.71: 507 (1980); F. Mark and F. Rosicky, ibid, 74: 562 (1980).
Y.K. Kim, Phys. Rev. 154: 17 (1967); ibid 159: 190 (1967); T. Kagawa, ibid, A12: 2245 (1975); ibid, A22: 2340 (1980).
M. Reed and B. Simon, “Functional Analysis” Vol. 1., Sec VIII. 5 Academic Press, New York (1972).
G.W.F. Drake and S.P. Goldman, Phys. Rev. A23: 2093 (1981)
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© 1983 Plenum Press, New York
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Grant, I.P. (1983). Self-Consistency and Numerical Problems. In: Malli, G.L. (eds) Relativistic Effects in Atoms, Molecules, and Solids. NATO Advanced Science Institutes Series, vol 87. Springer, Boston, MA. https://doi.org/10.1007/978-1-4613-3596-2_5
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