x ∈ [0, ∞)
x ∈ (−∞, ∞)
1
x
N ((1+x2 )2
x ∈ (−∞, ∞)
x
1
N ((1+x2 )2
e−α|x|+iqx
x ∈ (−∞, ∞)
1 exp (iqx)
N
1+x2
1
N
Bereich
ψ(x)
Lösung zu UA4.2
1
α
16
pπ
32
pπ
q
2
pπ
N
0
8
3π
0
0
1
1
1
2α2
1
hψ | x | ψi hψ | x2 | ψi
1
q
1−
64
9π 2
√1
2α
1
∆x
0
0
h̄q
h̄q
hψ | p | ψi
3h̄2
3h̄2
h̄2 (α2 + q 2 )
√
√
3h̄
3h̄
αh̄
h̄
√
2
h̄2
2 (1
+ 2q 2 )
∆p
hψ | p2 | ψi
2
2
√
2 3
3(1− 642 )
9π
=1.83137
p
2
√
√
∆x ∆p
h̄/2