The Cauchy problem for Hartree-Fock time-dependent equations
The difference equation related to the problem of the hydrogen atom in a strong magnetic field.
The energy of heavy atoms according to Brown and Ravenhall: the Scott correction.
The Foldy-Wouthuysen transformation in the two-particle case
The ground state energy of relativistic one-electron atoms according to Jansen and Heß.
The inverse -body problem. A geometrical approach
The mathematics of large atoms
The mixed regularity of electronic wave functions multiplied by explicit correlation factors
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,...
The mixed regularity of electronic wave functions multiplied by explicit correlation factors***
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,...
The nonrelativistic limit for the Weyl quantized Hamlitonians and pseudo-differential operators.
The projected single-particle Dirac operator for Coulombic potentials.
The quantum 3D superparticle.
The smooth continuation method in optimal control with an application to quantum systems
The motivation of this article is double. First of all we provide a geometrical framework to the application of the smooth continuation method in optimal control, where the concept of conjugate points is related to the convergence of the method. In particular, it can be applied to the analysis of the global optimality properties of the geodesic flows of a family of Riemannian metrics. Secondly, this study is used to complete the analysis of two-level dissipative quantum systems, where the system...
The smooth continuation method in optimal control with an application to quantum systems
The motivation of this article is double. First of all we provide a geometrical framework to the application of the smooth continuation method in optimal control, where the concept of conjugate points is related to the convergence of the method. In particular, it can be applied to the analysis of the global optimality properties of the geodesic flows of a family of Riemannian metrics. Secondly, this study is used to complete the analysis of two-level dissipative quantum systems, where the system...
The spin of the ground state of an atom.
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.
The wave equation with one point interaction and the (linearized) classical electrodynamics of a point particle
Théorie de la diffusion pour un atome couplé à un champ quantique
Time as a quantum observable, canonically conjugated to energy, and foundations of self-consistent time analysis of quantum processes.
Time-space duality and Salam-Weinberg model
Topological quasi *-algebras and the time evolution of systems
We give here a survey of some recent results on applications of topological quasi *-algebras to the analysis of the time evolution of quantum systems with infinitely many degrees of freedom.