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pchemII.lecture26.Many-Electron_Atoms

pchemII.lecture26.Many-Electron_Atoms - Page 1 of 10 26...

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Page 1 of 10 Scott Kirkby Last revised: 17 March 2008 26. Many-Electron Atoms Suggested Reading: Chapter 13.4 of the text. Introduction: All the systems we have examined up to this point are sufficiently simple that we have been able to obtain rigorous analytical solutions for the eigenfunctions and eigenvalues of the Schrödinger equation describing them This happy state of affairs comes to an abrupt halt when we begin to investigate atoms and molecules containing more than one electron. From this point onward, we shall have to be content with approximate solutions. However, such solutions can often be as accurate as experimental measurement if enough effort is put into the calculation. The fact that things are about to become mush more difficult should not be a cause for concern. Consider an atom that contains a nucleus of mass m n with a positive charge of +Ze and N electrons. For this system, we have a total of N+1 particles, each of which can have kinetic energy. Consequently, we expect the quantum mechanical Hamiltonian to contain N+1 kinetic energy terms of the form (26-1) K.E. term h 2 2 m ------- 2 =
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