12_variation_perturbation_matrixhq

H11h 2 2 h12 2 4 2 s11s 2 2 s1 2 s11s 2 2 s12

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Unformatted text preview: 6 0.8 x 20 10/7/2013 1 Hamiltonian and Overlap Matrices in matrix elements ˆ H i , j f i Hf j d Si , j f i f j d 0.167 0.033 7.143 10 3 H 1.587 10 3 4 3.608 10 5 8.325 10 0.033 7.143 10 3 1.587 10 3 S 3.608 10 4 5 8.325 10 5 1.943 10 3 7.143 10 0.033 3 9.524 10 3 2.381 10 4 5.772 10 4 1.388 10 5 3.330 10 3 7.143 10 3 1.587 10 4 3.608 10 5 8.325 10 5 1.943 10 6 4.571 10 3 2.381 10 4 6.494 10 4 1.665 10 5 4.163 10 5 1.028 10 3 1.587 10 4 3.608 10 5 8.325 10 5 1.943 10 6 4.571 10 6 1.083 10 3 1.587 10 4 5.772 10 4 1.665 10 5 4.440 10 5 1.143 10 6 2.887 10 4 3.608 10 5 8.325 10 5 1.943 10 6 4.571 10 6 1.083 10 7 2.577 10 Basis 4 3.608 10 4 1.388 10 5 4.163 10 5 1.143 10 6 3.007 10 7 7.732 10 5 8.325 10 5 1.943 10 6 4.571 10 6 1.083 10 7 2.577 10 8 6.163 10 5 8.325 10 5 3.330 10 5 1.028 10 7 7.732 10 7 2.017 10 6 2.887 10 not diagonal 5 1.943 10 6 4.571 10 6 1.083 10 8 6.163 10 8 1.479 10 not orthogonal 7 2.577 10 If the basis functions were eigenfunctions of the Hamiltonian, then the Hamiltonian matrix and overlap matrix would be diagonal. Solving Schrödinger’s equation is “diagonalizing” the H matrix....
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