Heliumlecture - Quantum Monte-Carlo Helium atom H =" 1 2 1 2 2 2" 2 r 1" 2 r 2 1 r 12 We assume that we can first of all take the trial

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Unformatted text preview: Quantum Monte-Carlo-- Helium atom H = " 1 2 # 1 2 + # 2 2 ( ) " 2 r 1 " 2 r 2 + 1 r 12 We assume that we can first of all take the trial wave function, " T ( r 1 , r 2 ) = A exp #$ ( r 1 + r 2 ) [ ] If we first ignore electron-electron repulsion, we get " = 2/ a Where a is the Bohr radius Energy with and without electron-electron repulsion Computing energy without the 1/r 12 term we get -108.8eV Experimental result -78.98eV ! Obviously e-e repulsion important Including 1/r 12 term, but not optimizing α , we get -74.8eV Optimizing α =1.69/a (the atom swells a bit) With optimized α , we get -77.5eV… within about 1.5eV Energy with and without electron-electron repulsion Computing energy without the 1/r 12 term we get -108.8eV Experimental result -78.98eV ! Obviously e-e repulsion important Including 1/r 12 term, but not optimizing α , we get -74.8eV Optimizing α =1.69/a (the atom swells a bit) With optimized α , we get -77.5eV… within about 1.5eV Can go lower yet! Energy with added correlations...
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This note was uploaded on 08/08/2011 for the course PHZ 5156 taught by Professor Johnson,m during the Fall '08 term at University of Central Florida.

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Heliumlecture - Quantum Monte-Carlo Helium atom H =" 1 2 1 2 2 2" 2 r 1" 2 r 2 1 r 12 We assume that we can first of all take the trial

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