Chap8-SuppHW - Supplementary Home Work Problems Chapter 8...

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Supplementary Home Work Problems Chapter 8 S8.1 Indicate whether each of the functions is (i) symmetric, (ii) antisymmetric, or (iii) neither, with respect to electron exchange. Note: f and g are spatial functions. (a) (b) (c) (d) (e) S8.2 Write down the complete expression for the Coulomb Integral [J 1s2p ] and Exchange Integral [K 1s2p ] for the repulsive and exchange interactions between electrons in 1s and 2p orbitals, respectively. Give your answer in (i) “Bra-Ket” notation and (ii) standard double integral notation. 2 1 ) 2 ( ) 1 ( α f f 2 1 ) 2 ( ) 1 ( g f ] )[ 2 ( ) 1 ( 2 1 2 1 β - f f 2 1 )] 2 ( ) 1 ( ) 2 ( ) 1 ( [ f g g f + ] )][ 2 ( ) 1 ( ) 2 ( ) 1 ( [ 2 1 2 1 + - f g g f
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S8.3 Consider the Helium excited state configuration 1s 1 2p 1 . or (a) Calculate the result of operating on the spin portion of the wavefunction. (b) Assume that the spatial atomic orbitals, ,are orthonormal. Show that the spatial and spin wavefunctions are normalized
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Chap8-SuppHW - Supplementary Home Work Problems Chapter 8...

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