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Elements of Group Theory
Continuous Rotation Groups
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absorption angular momentum operators antisymmetric approximation assumed atomic orbitals basis functions basis set belong bond calculated closed shell coefficients commutes components configuration construct contains coordinate transformation corresponding Coulomb crystal field defined degeneracy density matrix diagonal diatomic molecules dipole eigenfunctions eigenvalues emission energy example expression given Hamiltonian Hartree-Fock Hence Hermitian hydrogen integral invariant irreducible representations irreducible tensor linear combinations LS coupling magnetic field matrix elements molecular orbitals momenta multiplet notation nuclear nuclei number of electrons obtained one-electron orbital angular momentum orthogonality parity particles Pauli principle perturbation photon polarization possible potential product representation properties quantum numbers radial respect result rotational levels satisfy Schrodinger equation Section selection rules shown in Fig singlet Slater determinant spectra spherical harmonics spin functions spin-orbit interaction splitting Table tensor of rank theorem tion transition triplet two-electron values vanish vector vibrational wave function Wigner-Eckart theorem written zero