Excited states for hydrogen ion molecule confined by a prolate spheroidal boxes: variational approach

The energy eigenvalues for confined H2+\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\text{H}}_{2}^{ + }$$\end{document} molecule are computed by using the variational method. The approach proposed here uses a trial molecular function for the ground state composed of a linear combination of atomic orbitals for confined hydrogen atom; for other states, we build the trial molecular eigenfunctions inspired in atomic orbitals and by using the orthogonality of the wave functions. The molecule is confined in an impenetrable prolate spheroidal box. The atomic orbital for 1s state is built from a previous suggestion inspired by the factorization of the Schrödinger equation, and for 2s state, we used the Gram–Schmidt process to build a trial atomic function orthogonal with 1s trial function. The main contribution of this work is to propose new wave functions to be used for the confined hydrogen ion molecule. The results obtained are in agreement with other results present in the literature, and the trial functions proposed here can be used to study other confined molecules.