Nodal structures of few electron atoms

Abstract

In this paper the nodal structure for He atom is revisited and a procedure for identifying the symmetry properties and nodal structure of the time and spin independent Schroedinger equation will be presented. Application are made to the few electron atoms, and explicit, new nodal surface equations given for states of various symmetries. In the construction of trial functions for variational calculations in quantum mechanics, and in the choice of nodal surfaces needed in Monte Carlo calculations to obtain fermion solutions to Schroedinger equation for spin independent Hamiltonians, the accuracy of the calculations can be strongly influenced by the initial choice of the trial functions. We incorporated these newly found nodal conditions in the trial functions and energy eigenvalues were calculated with a better accuracy for different symmetries.