. [. Bibliography and D. Albertini, Notions of controllability for bilinear multilevel quantum systems, IEEE Trans. Automat. Control, issue.8, pp.481399-1403, 2003.

]. C. Alt02 and . Altafini, Controllability of quantum mechanical systems by root space decomposition, J. Math. Phys, vol.43, issue.5, pp.2051-2062, 2002.

S. Avdonin and W. Moran, Ingham-type inequalities and Riesz bases of divided differences Mathematical methods of optimization and control of large-scale systems, Int. J. Appl. Math. Comput . Sci, vol.11, issue.4, pp.803-820, 2000.

R. [. Bloch, C. Brockett, and . Rangan, Finite Controllability of Infinite-Dimensional Quantum Systems, IEEE Transactions on Automatic Control, vol.55, issue.8
DOI : 10.1109/TAC.2010.2044273

URL : http://arxiv.org/pdf/quant-ph/0608075

J. [. Boscain, F. Gauthier, M. Rossi, and . Sigalotti, Approximate Controllability, Exact Controllability, and Conical Eigenvalue Intersections for Quantum Mechanical Systems, Communications in Mathematical Physics, vol.30, issue.4, pp.1225-1239, 2015.
DOI : 10.1007/978-3-642-57237-1_4

URL : https://hal.archives-ouvertes.fr/hal-00869706

P. [. Berkolaiko and . Kuchment, Introduction to quantum graphs, volume 186 of Mathematical Surveys and Monographs

C. Baiocchi, V. Komornik, and P. Loreti, Ingham-Beurling type theorems with weakened gap conditions, Acta Mathematica Hungarica, vol.97, issue.1/2, pp.55-95, 2002.
DOI : 10.1023/A:1020806811956

C. [. Beauchard and . Laurent, Local controllability of 1D linear and nonlinear Schrödinger equations with bilinear control, J. Math. Pures Appl, issue.95, pp.94520-554, 2010.
DOI : 10.1016/j.matpur.2010.04.001

URL : https://doi.org/10.1016/j.matpur.2010.04.001

C. Bardos, G. Lebeau, and J. Rauch, Sharp Sufficient Conditions for the Observation, Control, and Stabilization of Waves from the Boundary, SIAM Journal on Control and Optimization, vol.30, issue.5, pp.1024-1065, 1992.
DOI : 10.1137/0330055

A. [. Baudouin and . Mercado, An inverse problem for Schrödinger equations with discontinuous main coefficient, Appl. Anal, vol.87, pp.10-111145, 2008.
DOI : 10.1080/00036810802140673

URL : http://arxiv.org/pdf/0804.1714

J. [. Ball, M. Marsden, and . Slemrod, Controllability for Distributed Bilinear Systems, SIAM Journal on Control and Optimization, vol.20, issue.4, pp.575-597, 1982.
DOI : 10.1137/0320042

URL : https://authors.library.caltech.edu/4635/1/BALsiamjco82.pdf

]. R. Bro73 and . Brockett, Lie theory and control systems defined on spheres Lie algebras: applications and computational methods, SIAM J. Appl. Math, vol.25, pp.213-225, 1972.

]. N. Bur91 and . Burq, Contrôle de l'´ equation de Schrödinger en présence d'obstacles strictement convexes, Journées " ´ Equations aux Dérivées Partielles, 1991.

E. [. Cerpa and . Crépeau, Boundary controllability for the nonlinear Korteweg???de Vries equation on any critical domain, Annales de l'Institut Henri Poincare (C) Non Linear Analysis, vol.26, issue.2, pp.457-475, 2009.
DOI : 10.1016/j.anihpc.2007.11.003

URL : https://hal.archives-ouvertes.fr/hal-00678473

, Periodic excitations of bilinear quantum systems

J. Automatica and . Ifac, , pp.2040-2046, 2012.

P. [. Chambrion, M. Mason, U. Sigalotti, and . Boscain, Controllability of the discrete-spectrum Schr??dinger equation driven by an external field, Annales de l'Institut Henri Poincare (C) Non Linear Analysis, vol.26, issue.1, pp.329-349, 2009.
DOI : 10.1016/j.anihpc.2008.05.001

]. J. Cor07 and . Coron, Control and nonlinearity, volume 136 of Mathematical Surveys and Monographs, 2007.

]. E. Dav95 and . Davies, Spectral theory and differential operators, volume 42 of Cambridge Studies in Advanced Mathematics, 1995.

B. Dehman, P. Gérard, and G. Lebeau, Stabilization and Control for the Nonlinear Schr??dinger Equation on a Compact Surface, Mathematische Zeitschrift, vol.69, issue.1, pp.729-749, 2006.
DOI : 10.5802/aif.652

E. [. Dáger and . Zuazua, Wave propagation, observation and control in 1-d flexible multi-structures, ) [Mathematics & Applications, 2006.

C. Fabre, Résultats de contrôlabilité exacte interne pour l'´ equation de Schrödinger et leurs limites asymptotiques: applicationàcationà certaineséquationscertaineséquations de plaques vibrantes Asymptotic Anal BIBLIOGRAPHY [Gru16] G. Grubb. Regularity of spectral fractional Dirichlet and Neumann problems, Math. Nachr, vol.5, issue.2897, pp.343-379831, 1992.

]. T. Kat53 and . Kato, Integration of the equation of evolution in a Banach space, J. Math. Soc. Japan, vol.5, pp.208-234, 1953.

]. T. Kat95 and . Kato, Perturbation theory for linear operators, Classics in Mathematics, 1995.

P. [. Komornik and . Loreti, Fourier series in control theory, 2005.
URL : https://hal.archives-ouvertes.fr/hal-00086863

]. P. Kuc04 and . Kuchment, Quantum graphs. I. Some basic structures. Waves Random Media, pp.107-128, 2004.

]. C. Lau10a and . Laurent, Global controllability and stabilization for the nonlinear Schrödinger equation on an interval, ESAIM Control Optim . Calc. Var, vol.16, issue.2, pp.356-379, 2010.

]. C. Lau10b and . Laurent, Global controllability and stabilization for the nonlinear Schrödinger equation on some compact manifolds of dimension 3, SIAM J. Math. Anal, vol.42, issue.2, pp.785-832, 2010.

]. G. Leb92 and . Lebeau, Contrôle de l'´ equation de Schrödinger, J. Math. Pures Appl, vol.71, issue.93, pp.267-291, 1992.

, Lions. Contrôle des systèmes distribués singuliers of Méthodes Mathématiques de l'Informatique [Mathematical Methods of Information Science]. Gauthier-Villars, 1983.

R. [. Lasiecka and . Triggiani, Optimal regularity, exact controllability and uniform stabilization of Schrödinger equations with Dirichlet control, Differential Integral Equations, vol.5, issue.3, pp.521-535, 1992.

H. [. Lange and . Teismann, Controllability of the nonlinear Schr??dinger equation in the vicinity of the ground state, Mathematical Methods in the Applied Sciences, vol.126, issue.13, pp.1483-1505, 2007.
DOI : 10.2140/pjm.1968.25.59

]. D. Lue69 and . Luenberger, Optimization by vector space methods, 1969.

]. E. Mac94 and . Machtyngier, Exact controllability for the Schrödinger equation, SIAM J. Control Optim, vol.32, issue.1, pp.24-34, 1994.

]. M. Mir09 and . Mirrahimi, Lyapunov control of a quantum particle in a decaying potential, Ann. Inst. H. Poincaré Anal. Non Linéaire, vol.26, issue.5, pp.1743-1765, 2009.

V. [. Morancey and . Nersesyan, Simultaneous global exact controllability of an arbitrary number of 1d bilinear Schr??dinger equations, Journal de Math??matiques Pures et Appliqu??es, vol.103, issue.1, pp.228-254, 2015.
DOI : 10.1016/j.matpur.2014.04.002

A. Mercado, A. Osses, and L. Rosier, Inverse problems for the Schr??dinger equation via Carleman inequalities with degenerate weights, Inverse Problems, vol.24, issue.1, p.15017, 2008.
DOI : 10.1088/0266-5611/24/1/015017

]. M. Mor14 and . Morancey, Simultaneous local exact controllability of 1D bilinear Schrödinger equations, Ann. Inst. H. Poincaré Anal. Non Linéaire, vol.31, issue.3, pp.501-529, 2014.

]. V. Ner09 and . Nersesyan, Growth of Sobolev norms and controllability of the Schrödinger equation, Comm. Math. Phys, vol.290, issue.1, pp.371-387, 2009.

]. V. Ner10 and . Nersesyan, Global approximate controllability for Schrödinger equation in higher Sobolev norms and applications, Ann. Inst. H. Poincaré Anal. Non Linéaire, vol.27, issue.3, pp.901-915, 2010.

H. [. Nersesyan and . Nersisyan, Global exact controllability in infinite time of Schr??dinger equation, Journal de Math??matiques Pures et Appliqu??es, vol.97, issue.4, pp.295-317, 2012.
DOI : 10.1016/j.matpur.2011.11.005

]. L. Ros97 and . Rosier, Exact boundary controllability for the Korteweg-de Vries equation on a bounded domain, ESAIM Control Optim. Calc. Var, vol.2, pp.33-55, 1997.

]. K. Rot56 and . Roth, Rational approximations to algebraic numbres, pp.119-126, 1955.

B. [. Reed and . Simon, Methods of modern mathematical physics. I, 1980.

B. [. Russell and . Zhang, Exact controllability and stabilizability of the Korteweg-de Vries equation, Transactions of the American Mathematical Society, vol.348, issue.09, pp.3643-3672, 1996.
DOI : 10.1090/S0002-9947-96-01672-8

B. [. Rosier and . Zhang, Local Exact Controllability and Stabilizability of the Nonlinear Schr??dinger Equation on a Bounded Interval, SIAM Journal on Control and Optimization, vol.48, issue.2, pp.972-992, 2009.
DOI : 10.1137/070709578

]. Sac00, . L. Yu, and . Sachkov, Controllability of invariant systems on Lie groups and homogeneous spaces, J. Math. Sci, vol.100, issue.8, pp.2355-2427, 2000.

]. H. Tri95 and . Triebel, Interpolation theory, function spaces, differential operators, 1995.

]. G. Tur00 and . Turinici, On the controllability of bilinear quantum systems, Mathematical models and methods for ab initio quantum chemistry, pp.75-92

. Springer and . Berlin, , 2000.

R. M. Young, An introduction to nonharmonic Fourier series , volume 93 of Pure and Applied Mathematics, 1980.

]. B. Zha99 and . Zhang, Exact boundary controllability of the Korteweg-de Vries equation, SIAM J. Control Optim, vol.37, issue.2, pp.543-565, 1999.

]. E. Zua93 and . Zuazua, Exact controllability for semilinear wave equations in one space dimension, Ann. Inst. H. Poincaré Anal. Non Linéaire, vol.10, issue.1, pp.109-129, 1993.