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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***

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,...

The nonrelativistic limit for the Weyl quantized Hamlitonians and pseudo-differential operators.

Michihiro Nagase, Tomio Umeda (1992)

Forum mathematicum

The projected single-particle Dirac operator for Coulombic potentials.

Jakubassa-Amundsen, D.H. (2005)

Documenta Mathematica

The quantum 3D superparticle.

Mezincescu, Luca, Townsend, Paul K. (2011)

SIGMA. Symmetry, Integrability and Geometry: Methods and Applications [electronic only]

The smooth continuation method in optimal control with an application to quantum systems

Bernard Bonnard, Nataliya Shcherbakova, Dominique Sugny (2011)

ESAIM: Control, Optimisation and Calculus of Variations

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

Bernard Bonnard, Nataliya Shcherbakova, Dominique Sugny (2011)

ESAIM: Control, Optimisation and Calculus of Variations

The spin of the ground state of an atom.

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.

The wave equation with one point interaction and the (linearized) classical electrodynamics of a point particle

Diego Noja, Andrea Posilicano (1998)

Annales de l'I.H.P. Physique théorique

Théorie de la diffusion pour un atome couplé à un champ quantique

Christian Gérard (1996/1997)

Séminaire Équations aux dérivées partielles

Time as a quantum observable, canonically conjugated to energy, and foundations of self-consistent time analysis of quantum processes.

Olkhovsky, V.S. (2009)

Advances in Mathematical Physics

Time-space duality and Salam-Weinberg model

Souček, J., Souček, V. (1980)

Abstracta. 8th Winter School on Abstract Analysis

Topological quasi *-algebras and the time evolution of $Q M_{\infty}$ systems

Fabio Bagarello (2005)

Banach Center Publications

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.

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