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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 Monte-Carlo simulation with atomic physics. In particular, we will use Monte-Carlo techniques to estimate the ground-state 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 ground-state solution satisfies H ( ~ r 1 ,~ r 2 ) = E ( ~ r 1 ,~ r 2 ) where E is the ground-state energy. For any trial wave function T ( ~ r 1 ,~ r 2 ) different from the ground-state 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