Dimension-dependent two-electron Hamiltonian matrix elements

Since the birth of quantum mechanics the ground state electronic energy of the two-electron atom has received special attention. This is because the t wo-electron system is the simplest atom to include electron-electron intera ctions. 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 dimens ion, D. The basis functions are the D-dependent hydrogenic wavefunctions: { 1s(2),2p(2),3d(2),4f(2)}. The electron-electron repulsion integrals are sol ved by the Fourier integral transform.