Many problems in quantum chemistry deal with the computation of fundamental or excited states of molecules and lead to the resolution of eigenvalue problems. One of the major difficulties in these computations lies in the very large dimension of the systems to be solved. Indeed these eigenfunctions depend on variables where stands for the number of particles (electrons and/or nucleari) in the molecule. In order to diminish the size of the systems to be solved, the chemists have proposed many...
Many problems in quantum
chemistry deal with the computation of fundamental or excited states of
molecules and lead to the resolution of eigenvalue problems. One of the
major difficulties in these computations lies in the very large
dimension of the systems to be solved. Indeed these eigenfunctions depend
on variables where stands for the number of particles
(electrons and/or nucleari) in the molecule. In order to diminish the size
of the systems to be solved, the chemists have proposed many
interesting...
This paper considers the inversion problem related to the
manipulation of quantum
systems using laser-matter interactions. The focus
is on the identification of the field free Hamiltonian and/or
the dipole moment of a
quantum system. The evolution of the system is given by the Schrödinger
equation. The available data are observations as a function of time
corresponding to dynamics generated by electric fields. The
well-posedness of the problem is proved, mainly focusing on the uniqueness of
the...
The convergence and efficiency of the reduced basis method used for the approximation of the solutions to a class of problems written as a parametrized PDE depends heavily on the choice of the elements that constitute the “reduced basis”. The purpose of this paper is to analyze the convergence for one of the approaches used for the selection of these elements, the greedy algorithm. Under natural hypothesis on the set of all solutions to the problem obtained when the parameter varies, we prove that...
The convergence and efficiency of the reduced basis method used for the approximation of the solutions to a class of problems written as a parametrized PDE depends heavily on the choice of the elements that constitute the “reduced basis”. The purpose of this paper is to analyze the convergence for one of the approaches used for the selection of these elements, the greedy algorithm. Under natural hypothesis on the set of all solutions to the problem obtained when the parameter varies, we prove that...
The convergence and efficiency of the reduced basis method used for the approximation of the solutions to a class of problems written as a parametrized PDE depends heavily on the choice of the elements that constitute the “reduced basis”. The purpose of this paper is to analyze the convergence for one of the approaches used for the selection of these elements, the greedy algorithm. Under natural hypothesis on the set of all solutions to the problem obtained when the parameter varies, we prove that...
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