Dimension‐dependent two‐electron Hamiltonian matrix elements

Abstract

Since the birth of quantum mechanics the ground state electronic energy of the two‐electron atom has received special attention. This is because the two‐electron system is the simplest atom to include electron–electron interactions. These interactions are key to understanding many‐electron systems. This paper adds to the knowledge of two‐electron atoms by presenting closed form solutions for Hamiltonian matrix elements at arbitrary spatial dimension, $D$. The basis functions are the $D$‐dependent hydrogenic wavefunctions: $\left\{ {{\text{1s}}^{\text{2}} {\text{,2p}}^{\text{2}} {\text{,3d}}^{\text{2}} {\text{,4f}}^{\text{2}} } \right\}$. The electron–electron repulsion integrals are solved by the Fourier integral transform.