Biomedical Engineering Reference
In-Depth Information
0.8
0.8
0.8
1.599
1.599
0.8
1.599
2.399
2.399
2.399
2.399
1.599
0.8
1.599
1.599
3.198
3.198
1.599
1.599
3.198
3.998
3.198
3.998
3.998
3.998
3.198
3.198
2.399
3.198
0.8
1.599
3.198
0.8
1.599
2.399
0.8
0.8
2.399
2.399
0.8
2.399
2.399
1.599
1.599
1.599
0.8
0.8
0.8
Figure 12.11
(
Ψ
2,1
)
2
versus x
A
and x
B
The labels
symmetric
and
antisymmetric
arise from the fact that interchange of the particle
names leaves the first combination unchanged but leads to a reversal of sign in the second
combination.
The resulting probability maps are shown in Figures 12.12 and 12.13.
In the symmetric state the maximum probability occurs at the points for which
x
A
=
x
B
=
L
/4or3
L
/4 and quite generally the probability is large only if the difference between
the particles is small.
The antisymmetric state is quite different; the probability is zero everywhere along the
diagonal (which corresponds to
x
A
x
B
) and the probability maxima occur at positions
where the two particles are far apart. I must emphasize that this apparent attraction and
repulsion between particles has nothing whatever to do with the forces between them;
indeed, we assumed at the start that the particles did not interact with each other. It certainly
is not an additional force in nature; it is simply to do with the indistinguishability of particles
and the symmetry of the wavefunction describing them. Like the zero-point vibrational
energy, this is a purely quantum mechanical effect and has no 'explanation' in classical
physics.
=
