Pré-Publication, Document De Travail (Preprint/Prepublication) Année : 2026

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.

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Dates et versions

hal-04589758 , version 1 (27-05-2024)
hal-04589758 , version 2 (09-09-2025)
hal-04589758 , version 3 (03-04-2026)

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Mi-Song Dupuy, Virginie Ehrlacher, Clément Guillot. A space-time variational formulation for the many-body electronic Schrödinger evolution equation. 2026. ⟨hal-04589758v3⟩
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