2202-2203 / 2239
Rotational symmetrical 3D Gauss – we can substitute for radius
(
)
(
)
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
e
e
e
PDF , , ,
2
2
2
e
PDF ,
y
z
r
x
x y z
x y z r
r
Σ
Σ
Σ
Σ
Σ
π Σ π Σ π Σ
Σ
−
−
−
−
=
⋅
⋅
+ + →
=
( )
3
3
2
2
π Σ
[
]
(
)
( )
( )
2
2
2
2
3
3
shell volume at
2
e
Pr
,
d
4 d
2
r
r
r
r r r r
r r
Σ
π
π Σ
−
∈ + =
⋅
123
14243
Probability that we find something in a spherical shell [
r
,
r
+d
r
]:
1
2
3
4
0.1
0.2
0.3
0.4
0.5
0.6
0 1 2 3 4
r
/
Σ