Chapter5_8 - PHY4604 R D Field Department of Physics Chapter5_8 University of Florida Helium(1 After hydrogen the simplest atom is helium 4 He 2

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Unformatted text preview: PHY4604 R. D. Field Department of Physics Chapter5_8.doc University of Florida Helium (1) After hydrogen the simplest atom is helium 4 He 2 ( i.e. Z = 2). The Hamiltonian is given by | | 2 2 2 2 | | 2 2 ) ( 2 2 ) ( 2 1 2 2 2 2 2 2 1 2 2 1 2 2 1 2 2 2 2 2 1 2 2 1 r r Ke r Ke m r Ke m r r Ke r Ke m p r Ke m p H op op op r r h h r r − + + ∇ − + + ∇ − = − + − + − = Electron-Electron Repulsion: The differential equation is too difficult to solve unless we neglect the electron-electron interaction term (not a good approximation but we will do it anyway). If we drop the term | | / 2 1 2 r r Ke r r − then the equation separates into two “hydrogen-like” wave functions but with 2 2 2 2 r Ke m r e He = = h and 2 2 2 4 ) ( 4 2 1 2 2 1 E c m r Ke E e He He = − = − = α where r is the Bohr radius and E is the ground state energy of hydrogen....
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This note was uploaded on 05/29/2011 for the course PHY 4064 taught by Professor Fields during the Spring '07 term at University of Florida.

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