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Quantum Engi Q and A_Part_25

# Quantum Engi Q and A_Part_25 - 5.7 WAYS TO SYMMETRIZE THE...

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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 symways-a Question: How many single-particle states would a basic Hartree-Fock approximation use to compute the electron structure of an arsenic atom? How many Slater determinants would that involve? Answer: Hartree-Fock would use 33 single-particle states, combining into a single Slater determinant. 5.7.2 Solution symways-b Question: If two more single-particle 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 34-th state would introduce 33 more Slater determinants, and the 35-th another 561, for a total of 595. 5.8 Matrix Formulation 5.8.1 Solution matfor-a Question: As a relatively simple example, work out the above ideas for the Q = 2 hydrogen molecule spatial states ψ S 1 = ψ l ψ r and ψ S 2 = ψ l ψ r . Write the matrix eigenvalue problem and identify the two eigenvalues and eigenvectors. Compare with the results of section 5.3. Assume that ψ l and ψ r have been slightly adjusted to be orthonormal. Then so are ψ S 1 and ψ S 2 orthonormal, since the various six-dimensional inner product integrals, like ( ψ S 1 | ψ S 2 ) ≡ ( ψ l ψ r | ψ r ψ l ) ≡ 74...
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Quantum Engi Q and A_Part_25 - 5.7 WAYS TO SYMMETRIZE THE...

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