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The Utility of Symmetry in Chemistry
The OneDimensional Wave Equation
Some Mathematical Apparatus
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angle angular momentum antisymmetric atomic orbitals axes axis basis functions basis vectors benzene bond character tables CN CN coefficients commute components configuration contains coordinates correlation corresponding cosets crystal degenerate diagonal dimension direct product displacements eigenfunctions eigenvalue electric dipole electronic energy equal equation equivalent example factor group Figure follows form a basis functions belong group elements group operators group theory Hamiltonian identical infinite number integral interaction invariant subgroup inversion irreducible representation isomorphic lattice linear combination matrix elements molecular orbitals molecule multiplication normal nuclear nuclei obtained one-dimensional orthogonal partner functions perturbing singlet plane point group point symmetry polar vector problem reducible result rotation group scalar product selection rules shown similarity transformation space group spectra spin functions spin-orbit coupling splitting symmetry operations tion transition triplet unit cell unitary unitary matrix vanish vibrational wavefunctions written zero