This section presents an approximate calculation of the energy levels for the helium atom as shown in [F171, problem 90]. We make use of a pure Coulomb Hamiltonian, i.e., no spin-dependent forces are included. The wavefunction separates into a spin part and a spatial part. We cannot ignore the spin part, however, as the requirement of an anti-symmetric (AS) two-electron wavefunction (Pauli principle) has to be satisfied. The wavefunction is given as a product of the coordinate space part that can be chosen to be symmetric (S), ψS, or AS, ψAS, under particle interchange times a two-particle spinor that again can be either S or AS, labeled χS and χAS, respectively. Thus, we can have an overall AS combination ψS × χAS or ψAS × χS.
KeywordsAngular Momentum Hydrogen Molecule Helium Atom Spin Part Internuclear Separation
Unable to display preview. Download preview PDF.