Nodal structures of few electron atoms

TL;DR

This paper revisits the nodal structures of the helium atom, providing explicit equations for various symmetries, which improve the accuracy of quantum mechanical calculations involving nodal surfaces.

Contribution

It introduces new explicit nodal surface equations for few-electron atoms, enhancing the construction of trial functions in variational and Monte Carlo methods.

Findings

Improved accuracy in energy calculations for different symmetries.

New explicit nodal surface equations for various states.

Enhanced trial functions for quantum calculations.

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.