2024/05/28 by Dupuy, Mi-Song, Ehrlacher, Virginie, Guillot, Clément · 1 citation
#FOS: Mathematics #Numerical Analysis (math.NA)
paper · doi:10.48550/arxiv.2405.18094
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.