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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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