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We compute the deficiency spaces of operators of the form $H_A{\hat {\otimes }} I + I{\hat {\otimes }} H_B$, for symmetric $H_A$ and self-adjoint $H_B$. This enables us to construct self-adjoint extensions (if they exist) by means of von Neumann's theory. The structure of the deficiency spaces for this case was asserted already in Ibort et al. [Boundary dynamics driven entanglement, J. Phys. A: Math. Theor.47(38) (2014) 385301], but only proven under the restriction of $H_B$ having discrete, non-degenerate spectrum.

This paper considers the inversion problem related to themanipulation of quantumsystems using laser-matter interactions. The focusis on the identification of the field free Hamiltonian and/orthe dipole moment of aquantum system. The evolution of the system is given by the Schrödingerequation. The available data are observations as a function of timecorresponding to dynamics generated by electric fields. Thewell-posedness of the problem is proved, mainly focusing on the uniqueness ofthe solution. A numerical approach is also introduced with anillustration of its efficiency on a test problem.

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Self-adjoint extensions of bipartite Hamiltonians

Hamiltonian identification for quantum systems: well-posedness and numerical approaches

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2 results

Self-adjoint extensions of bipartite Hamiltonians

Hamiltonian identification for quantum systems: well-posedness and numerical approaches