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REVIEW OF VECTORS VECTOR SPACES AND MATRICES
ABSTRACT GROUP THEORY
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Abelian angle angular momentum antisymmetric approximation atomic atomic orbitals axes axis basis functions belong Burnside's theorem calculate character table closed shells commute components configuration consider coordinates coupling crystal field cubic cubic field degeneracy determined dimensionality dipole transitions direct product effect eigenfunctions eigenvalues electrons energy equivalent example exchange integrals fact factor formula gives group elements group theory Hamiltonian Hartree interaction invariant irreducible representations L-S terms levels linear combinations magnetic matrix elements method molecular molecule multiplication normal notation nuclear nuclei obtain one-electron orthogonal parameters parity Pauli principle permutation perturbation Phys plane potential problem quantum mechanical quantum number Racah coefficients reduced result rotation group scalar secular equation selection rules similarity transformation simple spherical harmonics spin spin-orbit split structure subgroup symmetry group symmetry operations symmetry orbitals tensor terns transformation properties values vanish vector vibrational wavefunction Wigner coefficients