385lec27 - PHYS 385 Lecture 27 - Poly-electron atoms 27 - 1...

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Unformatted text preview: PHYS 385 Lecture 27 - Poly-electron atoms 27 - 1 2003 by David Boal, Simon Fraser University. All rights reserved; further copying or resale is strictly prohibited. Lecture 27 - Poly-electron atoms What's important : helium atom by approximation spin wavefunctions for helium Text : Gasiorowicz, Chap. 18 Helium atom We have now solved the Schrdinger equation for an arbitrary charge Z on the nucleus, and examined the specific case where Z = 1, the hydrogen atom. As long as there is only one electron present in the atom, these hydrogen-like solutions are perfectly valid for all Z . The next most complex atom (neutral) after hydrogen is helium. The relevant coordinates for the helium atom can be defined as The Hamiltonian operator for the atom then has the form: H = (- h 2 /2 m e ) [ 1 2 + 2 2 ] - 2 ke 2 / r N1- 2 ke 2 / r N2 + ke 2 / r 12 . Kinetic energies of attraction of repulsion electrons 1 & 2 electrons between (center of mass to nucleus electrons motion factored out) If the ke 2 / r 12 term were not present then we would have a separable 2-body problem which could be solved analytically. As it is, the Hamiltonian represents a three-body problem that must be solved numerically or by approximation. A nave approach to simplifying Hamiltonian is to see what effects the electrons have on each other. By and large, the electrons will not be closeby. Suppose for the moment that they are on opposite sides of the nucleus: e 1- +2 e e 2- charge on nucleus is +2 e e 1- r N2 e 2- r 12 r N1 PHYS 385 Lecture 27 - Poly-electron atoms 27 - 2 2003 by David Boal, Simon Fraser University. All rights reserved; further copying or resale is strictly prohibited. 2003 by David Boal, Simon Fraser University....
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385lec27 - PHYS 385 Lecture 27 - Poly-electron atoms 27 - 1...

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