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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 solution. A numerical approach is also introduced with an
illustration of its efficiency on a test problem.
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