A space-time variational formulation for the many-body electronic Schrödinger evolution equation
Résumé
We prove in this paper that the solution of the time-dependent Schrödinger equation can be expressed as the solution of a global space-time quadratic minimization problem that is amenable to Galerkin time-space discretization schemes, using an appropriate least-square formulation. The present analysis can be applied to the electronic many-body time-dependent Schrödinger equation with an arbitrary number of electrons and interaction potentials with Coulomb singularities. We motivate the interest of the present approach with two goals: first, the design of Galerkin space-time discretization methods; second, the definition of dynamical low-rank approximations following a variational principle different from the classical Dirac-Frenkel principle, and for which it is possible to prove the global-in-time existence of solutions.
Mots clés
- Schrodinger Equation
- Space-time variational formulation
- Many body interactions
- Coulomb potential
- Kato smoothness theory
- Schrödinger equation Space-time variational formulation MSC codes. 35A15 35Q41 35L15 65M15
- Schrödinger equation
- Space-time variational formulation MSC codes. 35A15
- 35Q41
- 35L15
- 65M15
Domaines
| Origine | Fichiers produits par l'(les) auteur(s) |
|---|---|
| licence |

