Biomedical Engineering Reference
In-Depth Information
0.593
1.778
1.185
2.37
1.185
3.555
0.593
4.148
2.37
0.593
2.963
4.148
1.778
2.37
3.555
2.37
1.185
1.778
2.963
0.593
1.778
0.593
1.778
1.185
1.185
2.37
1.185
0.593
3.555
0.593
2.963
4.148
0.593
2.963
2.963
2.37
3.555
4.148
1.778 2.37
2.963
1.778
1.185
1.778
0.593
1.185
0.593
Figure 12.13
Antisymmetric wavefunction squared
The first and the last are automatically symmetric with respect to interchange of the two
electron names, but the middle two are not satisfactory because they imply that the two
electrons can somehow be treated differently. Bearing the discussion of Section 12.6 in
mind, we construct two other spin functions that have definite spin symmetry properties.
Symmetric:
α (
s
A
) α (
s
B
)
1
2
(α (
s
A
) β (
s
B
)
β (
s
A
) α (
s
B
))
β (
s
A
) β (
s
B
)
+
Antisymmetric:
1
2
(α (
s
A
) β (
s
B
)
−
β (
s
A
) α (
s
B
))
If we had been considering two spinless particles, for example two alpha particles, there
would be no spin states and the above complications would not have arisen. We now have
to combine together the space and the spin wavefunctions. We do this by multiplying
