Dose 2016

Rotational symmetrical 3D Gauss – we can substitute for radius

2

2

2

y

x

z

−

−

−

2

2

2

2

2

2

Σ

Σ

Σ

e

e

e

(

)

PDF , , , x y z

Σ

=

⋅

⋅

2

2

2

π Σ π Σ π Σ

2

2

2

2

x y z r + + →

2

r

−

2

2

Σ

e

(

)

PDF , r

Σ

=

( ) 3

3

2 2 π Σ

0.6

0.5

Probability that we find something in a spherical shell [ r , r +d r ]:

0.4

2

0.3

r

−

2

2

e

Σ

0.2

(

)

2

[

]

Pr

,

d

4 d π 123 r r

r r r r ∈ + =

⋅

3

0.1

3

( ) 2

2 π Σ

shell volume at

r

14243

1

2

3

4

0 1 2 3 4 r / Σ

( ) r

PDF