Variational Treatment

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Variational Treatment Of Helium Atom
F. Grieman
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He atom - Variational Theory He atom Hamiltonian
in atomic units H (-½ ?12 Z/rN1)
(-½ ?22 Z/rN2) 1/r12 ?tr ? (want a
variable parameter) From P.T. we used ?o
?o1s(1) ?1s(2) C e-ZrN1 e-ZrN2 Suggest a
variable??? Zobs lt Z (other electron shielding
nucleus) Z as variable ?tr C e-ZrN1
e-ZrN2
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Hamiltonian
Trial ?
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-(Z)2
-(Z)2
-(Z)2
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Now what?
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(27/16)2 H
2.8477 H
Much better, but still not great. We must
improve the wave function.
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(No Transcript)
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Now via computer we can calculate atomic energies
very accurately. Should then be able to predict
atomic spectroscopy right on the money!!! In
fact, we do except !!!! EXTRA LINES are found
!!! ???
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The Sodium D1/D2 area, photographed through the
Phasmatron, at magnification 24x. You can
clearly see the D lines resolved
(marked below for reference).