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Éric Paturel (2000)
Journées équations aux dérivées partielles
In this paper we prove the existence of infinitely many solutions of the Dirac-Fock equations with electrons turning around a nucleus of atomic charge , satisfying and , where is the fundamental constant of the electromagnetic interaction (approximately 1/137). This work is an improvement of an article of Esteban-Séré, where the same result was proved under more restrictive assumptions on .
Caliari, Marco, Squassina, Marco (2008)
Electronic Journal of Differential Equations (EJDE) [electronic only]
Huber, Matthias (2009)
Documenta Mathematica
Graf, Gian Michele (1998)
Documenta Mathematica
Robnik, Marko, Romanovski, Valery G. (2007)
ETNA. Electronic Transactions on Numerical Analysis [electronic only]
Frank, Rupert L., Siedentop, Heinz, Warzel, Simone (2009)
Documenta Mathematica
Brummelhuis, Raymond, Siedentop, Heinz, Stockmeyer, Edgardo (2002)
Documenta Mathematica
Charles L. Fefferman, Luis A. Seco (1995)
Journées équations aux dérivées partielles
Harry Yserentant (2011)
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
The electronic Schrödinger equation describes the motion of N electrons under Coulomb interaction forces in a field of clamped nuclei. The solutions of this equation, the electronic wave functions, depend on 3N variables, three spatial dimensions for each electron. Approximating them is thus inordinately challenging. As is shown in the author's monograph [Yserentant, Lecture Notes in Mathematics 2000, Springer (2010)], the regularity of the solutions, which increases with the number of electrons,...
Harry Yserentant (2011)
ESAIM: Mathematical Modelling and Numerical Analysis
The electronic Schrödinger equation describes the motion of N electrons under Coulomb interaction forces in a field of clamped nuclei. The solutions of this equation, the electronic wave functions, depend on 3N variables, three spatial dimensions for each electron. Approximating them is thus inordinately challenging. As is shown in the author's monograph [Yserentant, Lecture Notes in Mathematics2000, Springer (2010)], the regularity of the solutions, which increases with the number of electrons,...
Jakubassa-Amundsen, D.H. (2005)
Documenta Mathematica
Charles L. Fefferman, Luis A. Seco (1996)
Revista Matemática Iberoamericana
In this paper we address a question posed by M. and T. Hoffmann-Ostenhof, which concerns the total spin of the ground state of an atom or molecule. Each electron is given a value for spin, ±1/2. The total spin is the sum of the individual spins.
Amandine Aftalion (2004/2005)
Séminaire Équations aux dérivées partielles
Antonio Córdoba, Charles L. Fefferman, Luis A. Seco (1995)
Revista Matemática Iberoamericana
We extend Van der Corput's method for exponential sums to study an oscillating term appearing in the quantum theory of large atoms. We obtain an interpretation in terms of classical dynamics and we produce sharp asymptotic upper and lower bounds for the oscillations.
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