Convergent iterative methods for the Hartree eigenproblem
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Volume 28 (1994) no. 5, p. 575-610
@article{M2AN_1994__28_5_575_0,
     author = {Auchmuty, G. and Jia, Wenyao},
     title = {Convergent iterative methods for the Hartree eigenproblem},
     journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Mod\'elisation Math\'ematique et Analyse Num\'erique},
     publisher = {Dunod},
     volume = {28},
     number = {5},
     year = {1994},
     pages = {575-610},
     zbl = {0821.65047},
     mrnumber = {1295588},
     language = {en},
     url = {http://www.numdam.org/item/M2AN_1994__28_5_575_0}
}
Auchmuty, G.; Jia, Wenyao. Convergent iterative methods for the Hartree eigenproblem. ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Volume 28 (1994) no. 5, pp. 575-610. http://www.numdam.org/item/M2AN_1994__28_5_575_0/

[1] J. P. Aubin, I. Ekeland, 1984, Applied Nonlinear Analysis, Wiley Interscience, New York. | MR 749753 | Zbl 0641.47066

[2] G. Auchmuty, 1983, Duality for Non-convex Variational Principles, J. Diff. Equations, 10, 80-145 | MR 717869 | Zbl 0533.49007

[3] G Auchmuty, 1989, Duality algorithms for nonconvex vanational principles, Numer. Funct. Anal. and Optim., 10, 211-264. | MR 989534 | Zbl 0646.49023

[4] P Blanchard, E. Brüning, 1992, Variational Methods in Mathematical Physics, Springer-Verlag. | MR 1230382 | Zbl 0756.49023

[5] I. Ekeland, R. Temam, 1974, Analyse Convexe et Problèmes Variationnels, Dunod, Paris | MR 463993 | Zbl 0281.49001

[6] I. Ekeland, T. Turnbull, 1983, Infinite-dimensional Optimization and Convexity, The Univ. of Chicago Press | MR 769469 | Zbl 0565.49003

[7] V Fock, 1930, Nächerungsmethode zur hösung der quantemechanischen Mehrkörper-problems, Z. Phys., 61, 126-148. | JFM 56.1313.08

[8] J. Froelich, personal communication.

[9] D. Gogny, P. L. Lions, 1987, Hartree-Fock theory in Nuclear Physics, RAIRO Modél. Math. Anal. Numér., 20, 571-637 | Numdam | MR 877058 | Zbl 0607.35078

[10] D. Hartree, 1928, The wave mechamcs of an atom with a non-Coulomb central field Part I. Theory and methods, Proc. Comb. Phil. Soc., 24, 89-312. | JFM 54.0966.05

[11] O Ladyzhenskaya, 1985, The Boundary Value Problems of Mathematical Physics, Springer-Verlag, New York. | MR 793735 | Zbl 0588.35003

[12] L. D Landau, E. M Lifshitz, 1965, Quantum Mechanics, Pergamon, 2nd ed. | Zbl 0178.57901

[13] E. H. Lieb, B. Simon, 1974, On solutions of the Hartree-Fock problem for atoms and molecules, J. Chem. Phys., 61, 735-736. | MR 408618

[14] E. H. Lieb, B. Simon, 1977, The Hartree-Fock theory for Coulomb Systems, Comm. Math. Phys., 53, 185-194. | MR 452286

[15] P. L. Lions, 1987, Hartree-Fock equations for Coulomb Systems, Comm. Math. Phys., 109, 33-97. | MR 879032 | Zbl 0618.35111

[16] P. L. Lions, 1989, On Hartree and Hartree-Fock equations in atomic and nuclear physics, Comp. Meth. Applied Mech. & Eng., 75, 53-60. | MR 1035746 | Zbl 0850.70012

[17] L. De Loura, 1986, A Numerical Method for the Hartree Equation of the Helium Atom, Calcolo, 23, 185-207. | MR 897628 | Zbl 0613.65139

[18] P. Quentin, H. Flocard, 1978, Self-consistent Calculations of Nuclear Properties with Phenomenological Effective Forces, Ann. Rev. Nucl. Part. Sci.,28, 523-596.

[19] M. Reed, B. Simon, 1980, Methods of Modern Mathematical Physics, Vol. III, Academic Press, New York. | MR 751959 | Zbl 0405.47007

[20] M. Reeken, 1970, General Theorem on Bifurcation and its Application to the Hartree Equation of the Helium Atom, J. Math. Phys., 11, 2505-2512. | MR 279648

[21] J. C. Slater, 1930, A note on Hartree's Method, Phys. Rev., 35, 210-211.

[22] E. Zeidler, 1986, Nonlinear Functional Analysis and its Applications I, Springer-Verlag, New York. | MR 816732 | Zbl 0583.47050

[23] E. Zeidler, 1985, Nonlinear Functional Analysis and its Applications III, Springer-Verlag, New York | MR 768749 | Zbl 0583.47051