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Statements
|
Ψ
3
(
x
,
y
,
z
)
|
2
=
2
7
/
4
5
1
/
4
∫
0
∞
ℜ
(
e
2
i
u
(
u
4
+
z
u
2
+
x
)
Ψ
2
(
2
7
/
4
5
1
/
4
y
u
3
/
4
,
2
u
5
(
3
z
+
10
u
2
)
)
)
d
u
u
1
/
4
.
superscript
canonical-integral
3
𝑥
𝑦
𝑧
2
superscript
2
7
4
superscript
5
1
4
superscript
subscript
0
2
𝑖
𝑢
superscript
𝑢
4
𝑧
superscript
𝑢
2
𝑥
canonical-integral
2
superscript
2
7
4
superscript
5
1
4
𝑦
superscript
𝑢
3
4
2
𝑢
5
3
𝑧
10
superscript
𝑢
2
𝑢
superscript
𝑢
1
4
{\displaystyle{\displaystyle|\Psi_{3}\left(x,y,z\right)|^{2}=\frac{2^{7/4}}{5^%
{1/4}}\int_{0}^{\infty}\Re\left({\mathrm{e}^{2iu(u^{4}+zu^{2}+x)}}\Psi_{2}%
\left(\frac{2^{7/4}}{5^{1/4}}yu^{3/4},\sqrt{\frac{2u}{5}}(3z+10u^{2})\right)%
\right)\frac{\mathrm{d}u}{u^{1/4}}.}}
Ψ
K
(
𝐱
)
canonical-integral
𝐾
𝐱
{\displaystyle{\displaystyle\Psi_{\NVar{K}}\left(\NVar{\mathbf{x}}\right)}}
d
x
𝑥
{\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
e
{\displaystyle{\displaystyle\mathrm{e}}}
i
imaginary-unit
{\displaystyle{\displaystyle\mathrm{i}}}
∫
{\displaystyle{\displaystyle\int}}
ℜ
absent
{\displaystyle{\displaystyle\Re}}
y
𝑦
{\displaystyle{\displaystyle y}}
z
𝑧
{\displaystyle{\displaystyle z}}
x
𝑥
{\displaystyle{\displaystyle x}}
Identifiers
