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

摘要

A set of displaced squeezed number states is proposed as trial wave functions in variational calculations ofro-vibrational energy levels of diatomic molecules. By employing the ladder-operator formalism, we constructsuch states as well as an algebraic Hamiltonian expressed in terms of normal-ordered boson operators. We alsoshow that this algebraic Hamiltonian can be expanded in terms of pseudoladder operators d(X , K) and cr(X , obtained via a generalized Bogoliubov transformation. In this case, the Hamiltonian matrix is built using theusual Fock basis set and the coherence and squeezing parameters X and K are optimized variationally. Theconvergence of the variational calculations is largely improved when using the displaced squeezed numberstates instead of the usual Fock ones. A class of generalized displaced squeezed number states is also consid-ered, and some numerical applications are given.