An application of the Brillouin–Löwdin perturbation expansion: Lower bounds to the energy eigenvalues of the rigid rotator in an electric field

Abstract

AbstractOne of the variants of Löwdin's partitioning technique that makes use of a Brillouin‐type perturbation expansion for the study of lower bounds to the eigenvalues of a Hamiltonian has not been applied to any practical quantum mechanical problem so far. To illustrate how powerful this method can be, an application is made to the rigid rotator in an electric field, which has already been studied by Choi and Smith using the bracketing function of an intermediate Hamiltonian. It turns out that for a given order of the basis set of the Bazley space the Brillouin–Löwdin perturbation expansion gives closer bounds than the method of Choi and Smith, except for the case l = m, where the procedures can be shown to be mathematically equivalent. Especially for high l − m the number of basis functions needed to attain the same accuracy is by far larger for the method of Choi and Smith than for the Brillouin–Löwdin method.