Volume 13, Number 2, April-June 2007
|Page(s)||378 - 395|
|Published online||12 May 2007|
Hamiltonian identification for quantum systems: well-posedness and numerical approaches
Rocquencourt B.P. 105, 78153 Le Chesnay Cedex, France.
2 CERMICS-ENPC, 6 & 8 Av. B. Pascal, 77455 Marne la Vallée Cedex, France; email@example.com
3 École des Mines de Paris, CAS, 60 Bd Saint-Michel, 75272 Paris Cedex 06, France; firstname.lastname@example.org
4 Department of Chemistry, Princeton University, Princeton, New Jersey 08544-1009; email@example.com
5 CEREMADE, Université Paris Dauphine, Place du Maréchal de Lattre de Tassigny, 75775 Paris Cedex 16, France; Gabriel.Turinici@dauphine.fr
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.
Mathematics Subject Classification: 93B30 / 65K10
Key words: Inverse problem / quantum systems / Hamiltonian identification / optimal identification
© EDP Sciences, SMAI, 2007
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