Biomedical Engineering Reference
In-Depth Information
-0.008
-0.008
80
-0.008
60
-0.086
0.075
0.158
0.117
-0.008
0.033
-0.008
-0.008
40
-0.008
20
-0.008
-0.008
0
0
20
40
60
80
Figure 13.5
Hydrogen 2s contour diagram
square root of
1 in an exponential factor) and it is usual to make use of the de Moivre
theorem in order to visualize the orbitals:
−
1
2
(exp (
j
φ)
=
+
−
cos φ
exp (
j
φ))
(13.31)
1
2
j
(exp (
j
φ)
sin φ
=
−
exp (
−
j
φ))
The
real equivalent
p-orbitals are therefore taken as linear combinations of
m
l
=+
1 and
−
1. Despite the name, they are not completely equivalent to the complex orbitals as only
the latter are eigenfunctions of the
z
component of the angular momentum. Luckily, this
only matters in the presence of an external magnetic field. The real equivalent 2p and 3p
orbitals are shown in Table 13.3.
These are usually represented as contour diagrams; the orbital shapes are memorable
because they are equivalent and point along the appropriate axes. Figure 13.6 shows a
hydrogenic 2p
z
orbital, which points along the vertical
z
axis.
