The Orbital Approximation Helium

In the helium atom, two electrons, each of charge —e, circle a nucleus with charge -h 2e (Fig. 1.7a). The wave function of the system must now allow for the results of simultaneous measurement of the positions of two electrons. Our wave function must tell us the probability of finding electron 1 in some 

FIGURE 1.7. (a) The helium atom (b) diagram to illustrate electron correlation 

By an obvious extension of our definition of the wave function for the hydrogen atom, the probability of simultaneously finding electron 1 in dz and electron 2 in dz2 must be given by 

If the electrons in helium did not repel each other, so that each moved freely in the field of the nucleus, the motion of each would then be the same as if the other electron were absent the probabilities of finding electron 1 in dti and electron 2 in dx2 would then be given hyil/i dzi and 1/ 2 dx2, respectively, where ij/i and ij/2 are hydrogenlike orbitals of the ion He . Comparison with equation (1.3) shows that in that case 

The helium atom would then again be representable in terms of an orbital picture, each electron occupying an orbital similar to one of the orbitals of hydrogen. 

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