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Vectors and Matrices
The Principal Axis Transformation
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angle angular momentum antisymmetric antiunitary antiunitary operators applies arbitrary assume atom axes calculation Chapter character coefficients commutes complex components configuration conjugate consider constant contains coordinate system corepresentation corresponding coset denoted determined diagonal matrix direct product eigen eigenfunctions eigenvalue energy equal equivalent expression follows formulas given group elements Hence Hermitian homomorphism identity implies integral invariant subgroup inversion irreducible representations isomorphic levels linear combinations linearly independent magnetic field magnetic quantum matrix elements multiplet system multiplication number of electrons obtain occur orbital quantum number orthogonal orthogonal matrix parameters particles permutation perturbation polarized pure rotation group quantities quantum mechanics repre result rotation group rows and columns scalar product Schrodinger equation sentation similarity transformation six-j symbols space spin coordinates substitution summation symmetric group tensor Theorem theory three-j symbols transition two-dimensional unitary group unitary matrix values vanish variables vector wave function Z-axis zero