12_variation_perturbation_matrixhq

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

This preview shows page 1. Sign up to view the full content.

This is the end of the preview. Sign up to access the rest of the document.

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....
View Full Document

{[ snackBarMessage ]}

Ask a homework question - tutors are online