Formalism of the displaced squeezed Fock states for variational calculations of highly excited ro-vibrational levels: Diatomic molecules

14 pagesInternational audienceA set of displaced squeezed number states is proposed as trial wave functions in variational calculations of ro-vibrational energy levels of diatomic molecules. By employing the ladder operator formalism, we construct such states as well as an algebraic Hamiltonian expressed in terms of normal-ordered boson operators. We also show that this algebraic Hamiltonian can be expanded in terms of pseudoladder operators a˜(), and a˜†(,) obtained via a generalized Bogoliubov transformation. In this case, the Hamiltonian matrix is built using the usual Fock basis set and the coherence and squeezing parameters and are optimized variationally. The convergence of the variational calculations is largely improved when using the displaced squeezed number states instead of the usual Fock ones. A class of generalized displaced squeezed number states is also considered, and some numerical applications are given