Atoms and Molecules

A₁ angular momentum operators antisymmetric approximation atom atomic orbitals axis B₁ basis functions basis set coefficients commutes components configuration contains Coulomb coupling crystal field defined degeneracy density matrix diagonal dipole E₁ eigenfunctions eigenvalues energy example expression H₂ Hamiltonian Hartree-Fock Hence hydrogen integral interaction irreducible representations irreducible tensor j₁ J₂ linear combinations m₁ magnetic field matrix elements molecular orbitals molecule momenta notation nuclear nuclei obtained one-electron orthogonality parity particles permutation perturbation photon potential product representation properties quantum numbers r₁ r₂ radial respect rotation S₁ satisfy Schrödinger equation Schrödinger representation Section Slater determinant spherical harmonics spin functions spin-orbit symmetry T₁ t₂ Table tensor of rank theorem tion transition U₁(t vector wave function Wigner-Eckart theorem written Y₁ zero Απ