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Unformatted text preview: 5.7. WAYS TO SYMMETRIZE THE WAVE FUNCTION 73 5.7 Ways to Symmetrize the Wave Function 5.7.1 Solution symwaysa Question: How many singleparticle states would a basic HartreeFock approximation use to compute the electron structure of an arsenic atom? How many Slater determinants would that involve? Answer: HartreeFock would use 33 singleparticle states, combining into a single Slater determinant. 5.7.2 Solution symwaysb Question: If two more singleparticle states would be used to improve the accuracy for the arsenic atom, (one more normally does not help), how many Slater determinants could be formed with those states? Answer: The 34th state would introduce 33 more Slater determinants, and the 35th another 561, for a total of 595. 5.8 Matrix Formulation 5.8.1 Solution matfora Question: As a relatively simple example, work out the above ideas for the Q = 2 hydrogen molecule spatial states S 1 = l r and S 2 = l r . Write the matrix eigenvalue problem and identify the two eigenvalues and eigenvectors. Compare with the results of section 5.3. Assume that l and r have been slightly adjusted to be orthonormal. Then so are S 1 and S 2 orthonormal, since the various sixdimensional inner product integrals, like ( S 1  S 2 ) ( l r  r l ) 74...
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 Fall '11
 GARVIN

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