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Unformatted text preview: Major Project: Ground state of the He atom PHZ 5156 This problem combines what we have learned about the technique of MonteCarlo simulation with atomic physics. In particular, we will use MonteCarlo techniques to estimate the groundstate wave function and energy of a helium atom. Remember a He atom has two electrons, two protons, and two neutrons. While the nucleus we can regard as a single particle for our purposes, the three body problem (nucleus and two electrons) does not allow for an exact analytical solution. The Hamiltonian for the problem in a set of units with  e  = 1 (i.e. the electron and proton charge), m = 1 and ~ = 1 is, H = 1 2 2 ~ r 1 1 2 2 ~ r 2 2 r 1 2 r 2 + 1 r 12 where r 1 =  ~ r 1  , r 2 =  ~ r 2  , and r 12 =  ~ r 1 ~ r 2  . The groundstate solution satisfies H ( ~ r 1 ,~ r 2 ) = E ( ~ r 1 ,~ r 2 ) where E is the groundstate energy. For any trial wave function T ( ~ r 1 ,~ r 2 ) different from the groundstate wave function ( ~ r 1 ,~ r 2 ), the energy expectation value given by E = R ......
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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.
 Fall '08
 Johnson,M

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