Chapter 13 - Variational calculations

Abstract

This chapter deals with the applications of the variational method to find bounds to the energy of ground and excited states of physical systems, in first and second order of perturbation theory, through the optimization of the variational parameters contained in the trial function. Optimization of nonlinear parameters using the Ransil’s method is considered for the ground and first excited state of the particle in the box with impenetrable walls, linear harmonic oscillator, one-electron atomic system, and ground state of the two-electron atomic system. Optimization of linear parameters using the Ritz’s method is considered for the 1s2s and 1s2p excited states of the He atom, and for the ground and excited state of the H2+ molecular ion. In the second order of perturbation theory, different variational approximations are considered for the dipole polarizability of the H atom in the ground state and for the C6 London dispersion coefficient in the long-range H–H interaction.