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

Abstract

A 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 $\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{a}(\ensuremath{\lambda},\ensuremath{\kappa})$ and ${\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{a}}^{\ifmmode\dagger\else\textdagger\fi{}}(\ensuremath{\lambda},\ensuremath{\kappa})$ 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 $\ensuremath{\lambda}$ and $\ensuremath{\kappa}$ 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.