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Unformatted text preview: Given the two eigenvalue equations Âφ n = a n φ n and Âφ m = a m φ m Multiply the first equation by φ m and integrate over all space. Then, take the complex conjugate of the second equation and multiply it by φ n , and integrate over all space. Subtract the two equations from each other and label this equation as (4 – 1). Given that by the definition of a Hermitian operator, discuss the two possibilities n=m and n≠m. In your explanation, make sure you prove that the eigenvalues are real numbers and that the two eigenfunctions are orthogonal. 3. The following are the three normalized sp 2 hybrid orbitals. Show that Ψ 1 is normalized and that Ψ 1 is orthogonal to Ψ 2 . Which orbital is missing from these equations and why is it missing?...
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This document was uploaded on 01/03/2012.
 Fall '09

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