2s: n=2,
ℓ
{\displaystyle \ell }
ψ
(
r
,
θ
,
ϕ
)
=
1
4
2
π
(
2
−
ρ
)
e
−
ρ
2
{\displaystyle \psi {\begin{pmatrix}r,\theta ,\phi \end{pmatrix}}={\frac {1}{4{\sqrt {2\pi }}}}{\begin{pmatrix}2-\rho \end{pmatrix}}e^{-{\frac {\rho }{2}}}}
2py : n=2,
ℓ
{\displaystyle \ell }
ψ
(
r
,
θ
,
ϕ
)
=
1
4
2
π
r
e
−
ρ
2
η
μ
θ
σ
υ
ν
ϕ
{\displaystyle \psi {\begin{pmatrix}r,\theta ,\phi \end{pmatrix}}={\frac {1}{4{\sqrt {2\pi }}}}re^{-{\frac {\rho }{2}}}\eta \mu \theta \sigma \upsilon \nu \phi }
2py : n=2,
ℓ
{\displaystyle \ell }
ψ
(
r
,
θ
,
ϕ
)
=
1
4
2
π
r
e
−
ρ
2
η
μ
θ
η
μ
ϕ
{\displaystyle \psi {\begin{pmatrix}r,\theta ,\phi \end{pmatrix}}={\frac {1}{4{\sqrt {2\pi }}}}re^{-{\frac {\rho }{2}}}\eta \mu \theta \eta \mu \phi }
2pz : n=2,
ℓ
{\displaystyle \ell }
ψ
(
r
,
θ
,
ϕ
)
=
1
4
2
π
r
e
−
ρ
2
σ
υ
ν
ϕ
{\displaystyle \psi {\begin{pmatrix}r,\theta ,\phi \end{pmatrix}}={\frac {1}{4{\sqrt {2\pi }}}}re^{-{\frac {\rho }{2}}}\sigma \upsilon \nu \phi }
3s: n=3,
ℓ
{\displaystyle \ell }
ψ
(
r
,
θ
,
ϕ
)
=
1
81
3
π
(
27
−
18
ρ
+
2
ρ
2
)
e
−
ρ
3
{\displaystyle \psi {\begin{pmatrix}r,\theta ,\phi \end{pmatrix}}={\frac {1}{81{\sqrt {3\pi }}}}{\begin{pmatrix}27-18\rho +2\rho ^{2}\end{pmatrix}}e^{-{\frac {\rho }{3}}}}
3px : n=3,
ℓ
{\displaystyle \ell }
ψ
(
r
,
θ
,
ϕ
)
=
2
81
2
π
r
(
6
−
ρ
)
e
−
ρ
3
η
μ
θ
σ
υ
ν
ϕ
{\displaystyle \psi {\begin{pmatrix}r,\theta ,\phi \end{pmatrix}}={\frac {2}{81{\sqrt {2\pi }}}}r{\begin{pmatrix}6-\rho \end{pmatrix}}e^{-{\frac {\rho }{3}}}\eta \mu \theta \sigma \upsilon \nu \phi }
3py : n=3,
ℓ
{\displaystyle \ell }
ψ
(
r
,
θ
,
ϕ
)
=
2
81
2
π
r
(
6
−
ρ
)
e
−
ρ
3
η
μ
θ
η
μ
ϕ
{\displaystyle \psi {\begin{pmatrix}r,\theta ,\phi \end{pmatrix}}={\frac {2}{81{\sqrt {2\pi }}}}r{\begin{pmatrix}6-\rho \end{pmatrix}}e^{-{\frac {\rho }{3}}}\eta \mu \theta \eta \mu \phi }
3pz : n=3,
ℓ
{\displaystyle \ell }
ψ
(
r
,
θ
,
ϕ
)
=
2
81
2
π
r
(
6
−
ρ
)
e
−
ρ
3
σ
υ
ν
ϕ
{\displaystyle \psi {\begin{pmatrix}r,\theta ,\phi \end{pmatrix}}={\frac {2}{81{\sqrt {2\pi }}}}r{\begin{pmatrix}6-\rho \end{pmatrix}}e^{-{\frac {\rho }{3}}}\sigma \upsilon \nu \phi }
3dz2 : n=3,
ℓ
{\displaystyle \ell }
ψ
(
r
,
θ
,
ϕ
)
=
1
81
6
π
r
2
e
−
ρ
3
(
3
σ
υ
ν
2
θ
−
1
)
{\displaystyle \psi {\begin{pmatrix}r,\theta ,\phi \end{pmatrix}}={\frac {1}{81{\sqrt {6\pi }}}}r^{2}e^{-{\frac {\rho }{3}}}{\begin{pmatrix}3\sigma \upsilon \nu ^{2}\theta -1\end{pmatrix}}}
3dzx : n=3,
ℓ
{\displaystyle \ell }
ψ
(
r
,
θ
,
ϕ
)
=
2
81
π
r
2
e
−
ρ
3
η
μ
θ
σ
υ
ν
θ
σ
υ
ν
ϕ
{\displaystyle \psi {\begin{pmatrix}r,\theta ,\phi \end{pmatrix}}={\frac {\sqrt {2}}{81{\sqrt {\pi }}}}r^{2}e^{-{\frac {\rho }{3}}}\eta \mu \theta \sigma \upsilon \nu \theta \sigma \upsilon \nu \phi }
3dyz : n=3,
ℓ
{\displaystyle \ell }
ψ
(
r
,
θ
,
ϕ
)
=
2
81
π
r
2
e
−
ρ
3
η
μ
θ
σ
υ
ν
θ
η
μ
ϕ
{\displaystyle \psi {\begin{pmatrix}r,\theta ,\phi \end{pmatrix}}={\frac {\sqrt {2}}{81{\sqrt {\pi }}}}r^{2}e^{-{\frac {\rho }{3}}}\eta \mu \theta \sigma \upsilon \nu \theta \eta \mu \phi }
3dx2 -y2 : n=3,
ℓ
{\displaystyle \ell }
ψ
(
r
,
θ
,
ϕ
)
=
1
81
2
π
ρ
2
e
−
ρ
3
η
μ
2
θ
σ
υ
ν
(
2
ϕ
)
{\displaystyle \psi {\begin{pmatrix}r,\theta ,\phi \end{pmatrix}}={\frac {1}{81{\sqrt {2\pi }}}}\rho ^{2}e^{-{\frac {\rho }{3}}}\eta \mu ^{2}\theta \sigma \upsilon \nu {\begin{pmatrix}2\phi \end{pmatrix}}}
3dxy : n=3,
ℓ
{\displaystyle \ell }
ψ
(
r
,
θ
,
ϕ
)
=
2
81
π
ρ
2
e
−
ρ
3
η
μ
2
θ
σ
υ
ν
ϕ
η
μ
ϕ
{\displaystyle \psi {\begin{pmatrix}r,\theta ,\phi \end{pmatrix}}={\frac {\sqrt {2}}{81{\sqrt {\pi }}}}\rho ^{2}e^{-{\frac {\rho }{3}}}\eta \mu ^{2}\theta \sigma \upsilon \nu \phi \eta \mu \phi }
4s: n=4,
ℓ
{\displaystyle \ell }
ψ
(
r
,
θ
,
ϕ
)
=
1
1536
π
(
192
−
144
ρ
+
24
ρ
2
−
ρ
3
)
e
−
ρ
4
{\displaystyle \psi {\begin{pmatrix}r,\theta ,\phi \end{pmatrix}}={\frac {1}{1536{\sqrt {\pi }}}}{\begin{pmatrix}192-144\rho +24\rho ^{2}-\rho ^{3}\end{pmatrix}}e^{-{\frac {\rho }{4}}}}
4px : n=4,
ℓ
{\displaystyle \ell }
ψ
(
r
,
θ
,
ϕ
)
=
1
256
5
π
r
(
80
−
20
ρ
−
ρ
2
)
e
−
ρ
4
η
μ
θ
σ
υ
ν
ϕ
{\displaystyle \psi {\begin{pmatrix}r,\theta ,\phi \end{pmatrix}}={\frac {1}{256{\sqrt {5\pi }}}}r{\begin{pmatrix}80-20\rho -\rho ^{2}\end{pmatrix}}e^{-{\frac {\rho }{4}}}\eta \mu \theta \sigma \upsilon \nu \phi }
4py : n=4,
ℓ
{\displaystyle \ell }
ψ
(
r
,
θ
,
ϕ
)
=
1
256
5
π
r
(
80
−
20
ρ
−
ρ
2
)
e
−
ρ
4
η
μ
θ
η
μ
ϕ
{\displaystyle \psi {\begin{pmatrix}r,\theta ,\phi \end{pmatrix}}={\frac {1}{256{\sqrt {5\pi }}}}r{\begin{pmatrix}80-20\rho -\rho ^{2}\end{pmatrix}}e^{-{\frac {\rho }{4}}}\eta \mu \theta \eta \mu \phi }
4pz : n=4,
ℓ
{\displaystyle \ell }
ψ
(
r
,
θ
,
ϕ
)
=
1
256
5
π
r
(
80
−
20
ρ
−
ρ
2
)
e
−
ρ
4
σ
υ
ν
ϕ
{\displaystyle \psi {\begin{pmatrix}r,\theta ,\phi \end{pmatrix}}={\frac {1}{256{\sqrt {5\pi }}}}r{\begin{pmatrix}80-20\rho -\rho ^{2}\end{pmatrix}}e^{-{\frac {\rho }{4}}}\sigma \upsilon \nu \phi }
4dz2 : n=4,
ℓ
{\displaystyle \ell }
ψ
(
r
,
θ
,
ϕ
)
=
1
3.072
π
r
2
(
12
−
ρ
)
e
−
ρ
4
(
3
σ
υ
ν
2
θ
−
1
)
{\displaystyle \psi {\begin{pmatrix}r,\theta ,\phi \end{pmatrix}}={\frac {1}{3.072{\sqrt {\pi }}}}r^{2}{\begin{pmatrix}12-\rho \end{pmatrix}}e^{-{\frac {\rho }{4}}}{\begin{pmatrix}3\sigma \upsilon \nu ^{2}\theta -1\end{pmatrix}}}
4dzx : n=4,
ℓ
{\displaystyle \ell }
ψ
(
r
,
θ
,
ϕ
)
=
3
1.536
π
r
2
(
12
−
ρ
)
e
−
ρ
4
η
μ
θ
σ
υ
ν
θ
σ
υ
ν
ϕ
{\displaystyle \psi {\begin{pmatrix}r,\theta ,\phi \end{pmatrix}}={\frac {\sqrt {3}}{1.536{\sqrt {\pi }}}}r^{2}{\begin{pmatrix}12-\rho \end{pmatrix}}e^{-{\frac {\rho }{4}}}\eta \mu \theta \sigma \upsilon \nu \theta \sigma \upsilon \nu \phi }
4dyz : n=4,
ℓ
{\displaystyle \ell }
ψ
(
r
,
θ
,
ϕ
)
=
3
1.536
π
r
2
(
12
−
ρ
)
e
−
ρ
4
η
μ
θ
σ
υ
ν
θ
η
μ
ϕ
{\displaystyle \psi {\begin{pmatrix}r,\theta ,\phi \end{pmatrix}}={\frac {\sqrt {3}}{1.536{\sqrt {\pi }}}}r^{2}{\begin{pmatrix}12-\rho \end{pmatrix}}e^{-{\frac {\rho }{4}}}\eta \mu \theta \sigma \upsilon \nu \theta \eta \mu \phi }
4dx2 -y2 : n=4,
ℓ
{\displaystyle \ell }
ψ
(
r
,
θ
,
ϕ
)
=
3
1.536
π
r
2
(
12
−
ρ
)
e
−
ρ
4
η
μ
2
θ
σ
υ
ν
(
2
ϕ
)
{\displaystyle \psi {\begin{pmatrix}r,\theta ,\phi \end{pmatrix}}={\frac {\sqrt {3}}{1.536{\sqrt {\pi }}}}r^{2}{\begin{pmatrix}12-\rho \end{pmatrix}}e^{-{\frac {\rho }{4}}}\eta \mu ^{2}\theta \sigma \upsilon \nu {\begin{pmatrix}2\phi \end{pmatrix}}}
4dxy : n=4,
ℓ
{\displaystyle \ell }
ψ
(
r
,
θ
,
ϕ
)
=
3
1.536
π
r
2
(
12
−
ρ
)
e
−
ρ
4
η
μ
2
θ
σ
υ
ν
ϕ
η
μ
ϕ
{\displaystyle \psi {\begin{pmatrix}r,\theta ,\phi \end{pmatrix}}={\frac {\sqrt {3}}{1.536{\sqrt {\pi }}}}r^{2}{\begin{pmatrix}12-\rho \end{pmatrix}}e^{-{\frac {\rho }{4}}}\eta \mu ^{2}\theta \sigma \upsilon \nu \phi \eta \mu \phi }
4fx3 : n=4,
ℓ
{\displaystyle \ell }
ψ
(
r
,
θ
,
ϕ
)
=
1
3.072
5
π
r
3
e
−
ρ
4
(
5
η
μ
2
θ
σ
υ
ν
2
ϕ
−
3
)
η
μ
θ
σ
υ
ν
ϕ
{\displaystyle \psi {\begin{pmatrix}r,\theta ,\phi \end{pmatrix}}={\frac {1}{3.072{\sqrt {5\pi }}}}r^{3}e^{-{\frac {\rho }{4}}}{\begin{pmatrix}5\eta \mu ^{2}\theta \sigma \upsilon \nu ^{2}\phi -3\end{pmatrix}}\eta \mu \theta \sigma \upsilon \nu \phi }
4fy3 : n=4,
ℓ
{\displaystyle \ell }
ψ
(
r
,
θ
,
ϕ
)
=
1
3.072
5
π
r
3
e
−
ρ
4
(
5
η
μ
2
θ
η
μ
2
ϕ
−
3
)
η
μ
θ
η
μ
ϕ
{\displaystyle \psi {\begin{pmatrix}r,\theta ,\phi \end{pmatrix}}={\frac {1}{3.072{\sqrt {5\pi }}}}r^{3}e^{-{\frac {\rho }{4}}}{\begin{pmatrix}5\eta \mu ^{2}\theta \eta \mu ^{2}\phi -3\end{pmatrix}}\eta \mu \theta \eta \mu \phi }
4fz3 : n=4,
ℓ
{\displaystyle \ell }
ψ
(
r
,
θ
,
ϕ
)
=
1
3.072
5
π
r
3
e
−
ρ
4
(
5
σ
υ
ν
2
θ
−
3
)
σ
υ
ν
θ
{\displaystyle \psi {\begin{pmatrix}r,\theta ,\phi \end{pmatrix}}={\frac {1}{3.072{\sqrt {5\pi }}}}r^{3}e^{-{\frac {\rho }{4}}}{\begin{pmatrix}5\sigma \upsilon \nu ^{2}\theta -3\end{pmatrix}}\sigma \upsilon \nu \theta }
4fx(z2 -y2 ) : n=4,
ℓ
{\displaystyle \ell }
ψ
(
r
,
θ
,
ϕ
)
=
3
3.072
π
r
3
e
−
ρ
4
(
σ
υ
ν
2
θ
−
η
μ
2
θ
η
μ
2
ϕ
)
η
μ
θ
σ
υ
ν
ϕ
{\displaystyle \psi {\begin{pmatrix}r,\theta ,\phi \end{pmatrix}}={\frac {\sqrt {3}}{3.072{\sqrt {\pi }}}}r^{3}e^{-{\frac {\rho }{4}}}{\begin{pmatrix}\sigma \upsilon \nu ^{2}\theta -\eta \mu ^{2}\theta \eta \mu ^{2}\phi \end{pmatrix}}\eta \mu \theta \sigma \upsilon \nu \phi }
4fy(z2 -x2 ) : n=4,
ℓ
{\displaystyle \ell }
ψ
(
r
,
θ
,
ϕ
)
=
3
3.072
π
r
3
e
−
ρ
4
(
σ
υ
ν
2
θ
−
η
μ
2
θ
σ
υ
ν
2
ϕ
)
η
μ
θ
η
μ
ϕ
{\displaystyle \psi {\begin{pmatrix}r,\theta ,\phi \end{pmatrix}}={\frac {\sqrt {3}}{3.072{\sqrt {\pi }}}}r^{3}e^{-{\frac {\rho }{4}}}{\begin{pmatrix}\sigma \upsilon \nu ^{2}\theta -\eta \mu ^{2}\theta \sigma \upsilon \nu ^{2}\phi \end{pmatrix}}\eta \mu \theta \eta \mu \phi }
4fz(x2 -y2 ) : n=4,
ℓ
{\displaystyle \ell }
ψ
(
r
,
θ
,
ϕ
)
=
3
3.072
π
r
3
e
−
ρ
4
(
1
−
2
η
μ
2
ϕ
)
σ
υ
ν
θ
η
μ
2
θ
{\displaystyle \psi {\begin{pmatrix}r,\theta ,\phi \end{pmatrix}}={\frac {\sqrt {3}}{3.072{\sqrt {\pi }}}}r^{3}e^{-{\frac {\rho }{4}}}{\begin{pmatrix}1-2\eta \mu ^{2}\phi \end{pmatrix}}\sigma \upsilon \nu \theta \eta \mu ^{2}\theta }
4fxyz : n=4,
ℓ
{\displaystyle \ell }
ψ
(
r
,
θ
,
ϕ
)
=
3
1536
π
r
3
e
−
ρ
4
σ
υ
ν
θ
η
μ
2
θ
σ
υ
ν
ϕ
η
μ
ϕ
{\displaystyle \psi {\begin{pmatrix}r,\theta ,\phi \end{pmatrix}}={\frac {\sqrt {3}}{1536{\sqrt {\pi }}}}r^{3}e^{-{\frac {\rho }{4}}}\sigma \upsilon \nu \theta \eta \mu ^{2}\theta \sigma \upsilon \nu \phi \eta \mu \phi }
5s: n=5,
ℓ
{\displaystyle \ell }
ψ
(
r
,
θ
,
ϕ
)
=
1
46.875
5
π
(
18.750
−
15.000
ρ
+
3.000
ρ
2
−
200
ρ
3
+
4
ρ
4
)
e
−
ρ
5
{\displaystyle \psi {\begin{pmatrix}r,\theta ,\phi \end{pmatrix}}={\frac {1}{46.875{\sqrt {5\pi }}}}{\begin{pmatrix}18.750-15.000\rho +3.000\rho ^{2}-200\rho ^{3}+4\rho ^{4}\end{pmatrix}}e^{-{\frac {\rho }{5}}}}
5px : n=5,
ℓ
{\displaystyle \ell }
ψ
(
r
,
θ
,
ϕ
)
=
1
46.875
10
π
r
(
7.500
−
2.250
ρ
+
180
ρ
2
−
4
ρ
3
)
e
−
ρ
5
η
μ
θ
σ
υ
ν
ϕ
{\displaystyle \psi {\begin{pmatrix}r,\theta ,\phi \end{pmatrix}}={\frac {1}{46.875{\sqrt {10\pi }}}}r{\begin{pmatrix}7.500-2.250\rho +180\rho ^{2}-4\rho ^{3}\end{pmatrix}}e^{-{\frac {\rho }{5}}}\eta \mu \theta \sigma \upsilon \nu \phi }
5py : n=5,
ℓ
{\displaystyle \ell }
ψ
(
r
,
θ
,
ϕ
)
=
1
46.875
10
π
r
(
7.500
−
2.250
ρ
+
180
ρ
2
−
4
ρ
3
)
e
−
ρ
5
η
μ
θ
η
μ
ϕ
{\displaystyle \psi {\begin{pmatrix}r,\theta ,\phi \end{pmatrix}}={\frac {1}{46.875{\sqrt {10\pi }}}}r{\begin{pmatrix}7.500-2.250\rho +180\rho ^{2}-4\rho ^{3}\end{pmatrix}}e^{-{\frac {\rho }{5}}}\eta \mu \theta \eta \mu \phi }
5pz : n=5,
ℓ
{\displaystyle \ell }
ψ
(
r
,
θ
,
ϕ
)
=
1
46.875
10
π
r
(
7.500
−
2.250
ρ
+
180
ρ
2
−
4
ρ
3
)
e
−
ρ
5
σ
υ
ν
θ
{\displaystyle \psi {\begin{pmatrix}r,\theta ,\phi \end{pmatrix}}={\frac {1}{46.875{\sqrt {10\pi }}}}r{\begin{pmatrix}7.500-2.250\rho +180\rho ^{2}-4\rho ^{3}\end{pmatrix}}e^{-{\frac {\rho }{5}}}\sigma \upsilon \nu \theta }
5dz2 : n=5,
ℓ
{\displaystyle \ell }
ψ
(
r
,
θ
,
ϕ
)
=
1
46.875
35
π
r
2
(
525
−
70
ρ
+
2
ρ
2
)
e
−
ρ
5
(
3
σ
υ
ν
2
θ
−
1
)
{\displaystyle \psi {\begin{pmatrix}r,\theta ,\phi \end{pmatrix}}={\frac {1}{46.875{\sqrt {35\pi }}}}r^{2}{\begin{pmatrix}525-70\rho +2\rho ^{2}\end{pmatrix}}e^{-{\frac {\rho }{5}}}{\begin{pmatrix}3\sigma \upsilon \nu ^{2}\theta -1\end{pmatrix}}}
5dzx : n=5,
ℓ
{\displaystyle \ell }
ψ
(
r
,
θ
,
ϕ
)
=
2
3
46.875
14
π
r
2
(
525
−
70
ρ
+
2
ρ
2
)
e
−
ρ
5
η
μ
θ
σ
υ
ν
θ
σ
υ
ν
ϕ
{\displaystyle \psi {\begin{pmatrix}r,\theta ,\phi \end{pmatrix}}={\frac {2{\sqrt {3}}}{46.875{\sqrt {14\pi }}}}r^{2}{\begin{pmatrix}525-70\rho +2\rho ^{2}\end{pmatrix}}e^{-{\frac {\rho }{5}}}\eta \mu \theta \sigma \upsilon \nu \theta \sigma \upsilon \nu \phi }
5dyz : n=5,
ℓ
{\displaystyle \ell }
ψ
(
r
,
θ
,
ϕ
)
=
2
3
46.875
14
π
r
2
(
525
−
70
ρ
+
2
ρ
2
)
e
−
ρ
5
η
μ
θ
σ
υ
ν
θ
η
μ
ϕ
{\displaystyle \psi {\begin{pmatrix}r,\theta ,\phi \end{pmatrix}}={\frac {2{\sqrt {3}}}{46.875{\sqrt {14\pi }}}}r^{2}{\begin{pmatrix}525-70\rho +2\rho ^{2}\end{pmatrix}}e^{-{\frac {\rho }{5}}}\eta \mu \theta \sigma \upsilon \nu \theta \eta \mu \phi }
5dx2 -y2 : n=5,
ℓ
{\displaystyle \ell }
ψ
(
r
,
θ
,
ϕ
)
=
3
46875
14
π
r
2
(
525
−
70
ρ
+
2
ρ
2
)
e
−
ρ
5
η
μ
2
θ
σ
υ
ν
(
2
ϕ
)
{\displaystyle \psi {\begin{pmatrix}r,\theta ,\phi \end{pmatrix}}={\frac {\sqrt {3}}{46875{\sqrt {14\pi }}}}r^{2}{\begin{pmatrix}525-70\rho +2\rho ^{2}\end{pmatrix}}e^{-{\frac {\rho }{5}}}\eta \mu ^{2}\theta \sigma \upsilon \nu {\begin{pmatrix}2\phi \end{pmatrix}}}
5dxy : n=5,
ℓ
{\displaystyle \ell }
ψ
(
r
,
θ
,
ϕ
)
=
2
3
46.875
14
π
r
2
(
525
−
70
ρ
+
2
ρ
2
)
e
−
ρ
5
η
μ
2
θ
σ
υ
ν
ϕ
η
μ
ϕ
{\displaystyle \psi {\begin{pmatrix}r,\theta ,\phi \end{pmatrix}}={\frac {2{\sqrt {3}}}{46.875{\sqrt {14\pi }}}}r^{2}{\begin{pmatrix}525-70\rho +2\rho ^{2}\end{pmatrix}}e^{-{\frac {\rho }{5}}}\eta \mu ^{2}\theta \sigma \upsilon \nu \phi \eta \mu \phi }
5fx3 : n=5,
ℓ
{\displaystyle \ell }
ψ
(
r
,
θ
,
ϕ
)
=
1
46.875
10
π
r
3
(
20
−
ρ
)
e
−
ρ
5
(
5
η
μ
2
θ
σ
υ
ν
2
ϕ
−
3
)
η
μ
θ
σ
υ
ν
ϕ
{\displaystyle \psi {\begin{pmatrix}r,\theta ,\phi \end{pmatrix}}={\frac {1}{46.875{\sqrt {10\pi }}}}r^{3}{\begin{pmatrix}20-\rho \end{pmatrix}}e^{-{\frac {\rho }{5}}}{\begin{pmatrix}5\eta \mu ^{2}\theta \sigma \upsilon \nu ^{2}\phi -3\end{pmatrix}}\eta \mu \theta \sigma \upsilon \nu \phi }
5fy3 : n=5,
ℓ
{\displaystyle \ell }
ψ
(
r
,
θ
,
ϕ
)
=
1
46.875
10
π
r
3
(
20
−
ρ
)
e
−
ρ
5
(
5
η
μ
2
θ
η
μ
2
ϕ
−
3
)
η
μ
θ
η
μ
ϕ
{\displaystyle \psi {\begin{pmatrix}r,\theta ,\phi \end{pmatrix}}={\frac {1}{46.875{\sqrt {10\pi }}}}r^{3}{\begin{pmatrix}20-\rho \end{pmatrix}}e^{-{\frac {\rho }{5}}}{\begin{pmatrix}5\eta \mu ^{2}\theta \eta \mu ^{2}\phi -3\end{pmatrix}}\eta \mu \theta \eta \mu \phi }
5fz3 : n=5,
ℓ
{\displaystyle \ell }
ψ
(
r
,
θ
,
ϕ
)
=
1
46.875
10
π
r
3
(
20
−
ρ
)
e
−
ρ
5
(
5
σ
υ
ν
2
θ
−
3
)
σ
υ
ν
θ
{\displaystyle \psi {\begin{pmatrix}r,\theta ,\phi \end{pmatrix}}={\frac {1}{46.875{\sqrt {10\pi }}}}r^{3}{\begin{pmatrix}20-\rho \end{pmatrix}}e^{-{\frac {\rho }{5}}}{\begin{pmatrix}5\sigma \upsilon \nu ^{2}\theta -3\end{pmatrix}}\sigma \upsilon \nu \theta }
5fx(z2 -y2 ) : n=5,
ℓ
{\displaystyle \ell }
ψ
(
r
,
θ
,
ϕ
)
=
3
46.875
2
π
r
3
(
20
−
ρ
)
e
−
ρ
5
(
σ
υ
ν
2
θ
−
η
μ
2
θ
η
μ
2
ϕ
)
η
μ
θ
σ
υ
ν
ϕ
{\displaystyle \psi {\begin{pmatrix}r,\theta ,\phi \end{pmatrix}}={\frac {\sqrt {3}}{46.875{\sqrt {2\pi }}}}r^{3}{\begin{pmatrix}20-\rho \end{pmatrix}}e^{-{\frac {\rho }{5}}}{\begin{pmatrix}\sigma \upsilon \nu ^{2}\theta -\eta \mu ^{2}\theta \eta \mu ^{2}\phi \end{pmatrix}}\eta \mu \theta \sigma \upsilon \nu \phi }
5fy(z2 -x2 ) : n=5,
ℓ
{\displaystyle \ell }
ψ
(
r
,
θ
,
ϕ
)
=
3
46.875
2
π
r
3
(
20
−
ρ
)
e
−
ρ
5
(
σ
υ
ν
2
θ
−
η
μ
2
θ
σ
υ
ν
2
ϕ
)
η
μ
θ
η
μ
ϕ
{\displaystyle \psi {\begin{pmatrix}r,\theta ,\phi \end{pmatrix}}={\frac {\sqrt {3}}{46.875{\sqrt {2\pi }}}}r^{3}{\begin{pmatrix}20-\rho \end{pmatrix}}e^{-{\frac {\rho }{5}}}{\begin{pmatrix}\sigma \upsilon \nu ^{2}\theta -\eta \mu ^{2}\theta \sigma \upsilon \nu ^{2}\phi \end{pmatrix}}\eta \mu \theta \eta \mu \phi }
5fz(x2 -y2 ) : n=5,
ℓ
{\displaystyle \ell }
ψ
(
r
,
θ
,
ϕ
)
=
3
46.875
2
π
r
3
(
20
−
ρ
)
e
−
ρ
5
(
1
−
2
η
μ
2
ϕ
)
σ
υ
ν
θ
η
μ
2
θ
{\displaystyle \psi {\begin{pmatrix}r,\theta ,\phi \end{pmatrix}}={\frac {\sqrt {3}}{46.875{\sqrt {2\pi }}}}r^{3}{\begin{pmatrix}20-\rho \end{pmatrix}}e^{-{\frac {\rho }{5}}}{\begin{pmatrix}1-2\eta \mu ^{2}\phi \end{pmatrix}}\sigma \upsilon \nu \theta \eta \mu ^{2}\theta }
5fxyz : n=5,
ℓ
{\displaystyle \ell }
ψ
(
r
,
θ
,
ϕ
)
=
2
3
46875
2
π
r
3
(
20
−
ρ
)
e
−
ρ
5
σ
υ
ν
θ
η
μ
2
θ
σ
υ
ν
ϕ
η
μ
ϕ
{\displaystyle \psi {\begin{pmatrix}r,\theta ,\phi \end{pmatrix}}={\frac {2{\sqrt {3}}}{46875{\sqrt {2\pi }}}}r^{3}{\begin{pmatrix}20-\rho \end{pmatrix}}e^{-{\frac {\rho }{5}}}\sigma \upsilon \nu \theta \eta \mu ^{2}\theta \sigma \upsilon \nu \phi \eta \mu \phi }
5gz4 : n=5,
ℓ
{\displaystyle \ell }
ψ
(
r
,
θ
,
ϕ
)
=
k
28.800
70
π
r
4
e
−
ρ
5
(
35
σ
υ
ν
4
θ
−
30
σ
υ
ν
2
θ
+
3
)
{\displaystyle \psi {\begin{pmatrix}r,\theta ,\phi \end{pmatrix}}={\frac {k}{28.800{\sqrt {70\pi }}}}r^{4}e^{-{\frac {\rho }{5}}}{\begin{pmatrix}35\sigma \upsilon \nu ^{4}\theta -30\sigma \upsilon \nu ^{2}\theta +3\end{pmatrix}}}
5gz2 x : n=5,
ℓ
{\displaystyle \ell }
ψ
(
r
,
θ
,
ϕ
)
=
k
28.800
70
π
r
4
e
−
ρ
5
(
4
σ
υ
ν
2
θ
−
3
η
μ
2
θ
σ
υ
ν
2
ϕ
−
3
η
μ
2
θ
η
μ
2
ϕ
)
η
μ
θ
σ
υ
ν
ϕ
σ
υ
ν
θ
{\displaystyle \psi {\begin{pmatrix}r,\theta ,\phi \end{pmatrix}}={\frac {k}{28.800{\sqrt {70\pi }}}}r^{4}e^{-{\frac {\rho }{5}}}{\begin{pmatrix}4\sigma \upsilon \nu ^{2}\theta -3\eta \mu ^{2}\theta \sigma \upsilon \nu ^{2}\phi -3\eta \mu ^{2}\theta \eta \mu ^{2}\phi \end{pmatrix}}\eta \mu \theta \sigma \upsilon \nu \phi \sigma \upsilon \nu \theta }
5gz2 y : n=5,
ℓ
{\displaystyle \ell }
ψ
(
r
,
θ
,
ϕ
)
=
k
28.800
70
π
r
4
e
−
ρ
5
(
4
σ
υ
ν
2
θ
−
3
η
μ
2
θ
σ
υ
ν
2
ϕ
−
3
η
μ
2
θ
η
μ
2
ϕ
)
η
μ
θ
η
μ
ϕ
σ
υ
ν
θ
{\displaystyle \psi {\begin{pmatrix}r,\theta ,\phi \end{pmatrix}}={\frac {k}{28.800{\sqrt {70\pi }}}}r^{4}e^{-{\frac {\rho }{5}}}{\begin{pmatrix}4\sigma \upsilon \nu ^{2}\theta -3\eta \mu ^{2}\theta \sigma \upsilon \nu ^{2}\phi -3\eta \mu ^{2}\theta \eta \mu ^{2}\phi \end{pmatrix}}\eta \mu \theta \eta \mu \phi \sigma \upsilon \nu \theta }
5gz2 xy : n=5,
ℓ
{\displaystyle \ell }
ψ
(
r
,
θ
,
ϕ
)
=
k
28.800
70
π
r
4
e
−
ρ
5
(
6
σ
υ
ν
2
θ
−
η
μ
2
θ
σ
υ
ν
2
ϕ
−
η
μ
2
θ
η
μ
2
ϕ
)
η
μ
2
θ
η
μ
ϕ
σ
υ
ν
ϕ
{\displaystyle \psi {\begin{pmatrix}r,\theta ,\phi \end{pmatrix}}={\frac {k}{28.800{\sqrt {70\pi }}}}r^{4}e^{-{\frac {\rho }{5}}}{\begin{pmatrix}6\sigma \upsilon \nu ^{2}\theta -\eta \mu ^{2}\theta \sigma \upsilon \nu ^{2}\phi -\eta \mu ^{2}\theta \eta \mu ^{2}\phi \end{pmatrix}}\eta \mu ^{2}\theta \eta \mu \phi \sigma \upsilon \nu \phi }
5gz2 (x2 -y2 ) : n=5,
ℓ
{\displaystyle \ell }
ψ
(
r
,
θ
,
ϕ
)
=
k
28.800
70
π
r
4
e
−
ρ
5
(
6
σ
υ
ν
2
θ
−
η
μ
2
θ
σ
υ
ν
2
ϕ
−
η
μ
2
θ
η
μ
2
ϕ
)
(
1
−
2
η
μ
2
ϕ
)
η
μ
2
θ
{\displaystyle \psi {\begin{pmatrix}r,\theta ,\phi \end{pmatrix}}={\frac {k}{28.800{\sqrt {70\pi }}}}r^{4}e^{-{\frac {\rho }{5}}}{\begin{pmatrix}6\sigma \upsilon \nu ^{2}\theta -\eta \mu ^{2}\theta \sigma \upsilon \nu ^{2}\phi -\eta \mu ^{2}\theta \eta \mu ^{2}\phi \end{pmatrix}}{\begin{pmatrix}1-2\eta \mu ^{2}\phi \end{pmatrix}}\eta \mu ^{2}\theta }
5gzx3 : n=5,
ℓ
{\displaystyle \ell }
ψ
(
r
,
θ
,
ϕ
)
=
k
28.800
70
π
r
4
e
−
ρ
5
η
μ
3
θ
σ
υ
ν
ϕ
σ
υ
ν
θ
(
1
−
4
η
μ
2
ϕ
)
{\displaystyle \psi {\begin{pmatrix}r,\theta ,\phi \end{pmatrix}}={\frac {k}{28.800{\sqrt {70\pi }}}}r^{4}e^{-{\frac {\rho }{5}}}\eta \mu ^{3}\theta \sigma \upsilon \nu \phi \sigma \upsilon \nu \theta {\begin{pmatrix}1-4\eta \mu ^{2}\phi \end{pmatrix}}}
5gzy3 : n=5,
ℓ
{\displaystyle \ell }
ψ
(
r
,
θ
,
ϕ
)
=
k
28.800
70
π
r
4
e
−
ρ
5
η
μ
3
θ
η
μ
ϕ
σ
υ
ν
θ
(
3
−
4
η
μ
2
ϕ
)
{\displaystyle \psi {\begin{pmatrix}r,\theta ,\phi \end{pmatrix}}={\frac {k}{28.800{\sqrt {70\pi }}}}r^{4}e^{-{\frac {\rho }{5}}}\eta \mu ^{3}\theta \eta \mu \phi \sigma \upsilon \nu \theta {\begin{pmatrix}3-4\eta \mu ^{2}\phi \end{pmatrix}}}
5gxy(x2 -y2 ) : n=5,
ℓ
{\displaystyle \ell }
ψ
(
r
,
θ
,
ϕ
)
=
k
28.800
70
π
r
4
e
−
ρ
5
η
μ
3
θ
σ
υ
ν
ϕ
σ
υ
ν
θ
(
1
−
2
η
μ
2
ϕ
)
{\displaystyle \psi {\begin{pmatrix}r,\theta ,\phi \end{pmatrix}}={\frac {k}{28.800{\sqrt {70\pi }}}}r^{4}e^{-{\frac {\rho }{5}}}\eta \mu ^{3}\theta \sigma \upsilon \nu \phi \sigma \upsilon \nu \theta {\begin{pmatrix}1-2\eta \mu ^{2}\phi \end{pmatrix}}}
5gx4 +y4 : n=5,
ℓ
{\displaystyle \ell }
ψ
(
r
,
θ
,
ϕ
)
=
k
28.800
70
π
r
4
e
−
ρ
5
η
μ
4
θ
(
1
−
4
σ
υ
ν
2
ϕ
η
μ
2
ϕ
)
{\displaystyle \psi {\begin{pmatrix}r,\theta ,\phi \end{pmatrix}}={\frac {k}{28.800{\sqrt {70\pi }}}}r^{4}e^{-{\frac {\rho }{5}}}\eta \mu ^{4}\theta {\begin{pmatrix}1-4\sigma \upsilon \nu ^{2}\phi \eta \mu ^{2}\phi \end{pmatrix}}}
6s: n=6,
ℓ
{\displaystyle \ell }
ψ
(
r
,
θ
,
ϕ
)
=
1
1.049.760
6
π
(
174.960
−
145.800
ρ
+
32.400
ρ
2
−
2.700
ρ
3
+
90
ρ
4
−
ρ
5
)
e
−
ρ
6
{\displaystyle \psi {\begin{pmatrix}r,\theta ,\phi \end{pmatrix}}={\frac {1}{1.049.760{\sqrt {6\pi }}}}{\begin{pmatrix}174.960-145.800\rho +32.400\rho ^{2}-2.700\rho ^{3}+90\rho ^{4}-\rho ^{5}\end{pmatrix}}e^{-{\frac {\rho }{6}}}}
6px : n=6,
ℓ
{\displaystyle \ell }
ψ
(
r
,
θ
,
ϕ
)
=
1
12.186
70
π
r
(
5.506.240
−
1.870.830
ρ
+
183.708
ρ
2
−
6.804
ρ
3
+
81
ρ
4
)
e
−
ρ
6
η
μ
θ
σ
υ
ν
ϕ
{\displaystyle \psi {\begin{pmatrix}r,\theta ,\phi \end{pmatrix}}={\frac {1}{12.186{\sqrt {70\pi }}}}r{\begin{pmatrix}5.506.240-1.870.830\rho +183.708\rho ^{2}-6.804\rho ^{3}+81\rho ^{4}\end{pmatrix}}e^{-{\frac {\rho }{6}}}\eta \mu \theta \sigma \upsilon \nu \phi }
6py : n=6,
ℓ
{\displaystyle \ell }
ψ
(
r
,
θ
,
ϕ
)
=
1
12.186
70
π
r
(
5.506.240
−
1.870.830
ρ
+
183.708
ρ
2
−
6.804
ρ
3
+
81
ρ
4
)
e
−
ρ
6
η
μ
θ
η
μ
ϕ
{\displaystyle \psi {\begin{pmatrix}r,\theta ,\phi \end{pmatrix}}={\frac {1}{12.186{\sqrt {70\pi }}}}r{\begin{pmatrix}5.506.240-1.870.830\rho +183.708\rho ^{2}-6.804\rho ^{3}+81\rho ^{4}\end{pmatrix}}e^{-{\frac {\rho }{6}}}\eta \mu \theta \eta \mu \phi }
6pz : n=6,
ℓ
{\displaystyle \ell }
ψ
(
r
,
θ
,
ϕ
)
=
1
12.186
70
π
r
(
5.506.240
−
1.870.830
ρ
+
183.708
ρ
2
−
6.804
ρ
3
+
81
ρ
4
)
e
−
ρ
6
σ
υ
ν
θ
{\displaystyle \psi {\begin{pmatrix}r,\theta ,\phi \end{pmatrix}}={\frac {1}{12.186{\sqrt {70\pi }}}}r{\begin{pmatrix}5.506.240-1.870.830\rho +183.708\rho ^{2}-6.804\rho ^{3}+81\rho ^{4}\end{pmatrix}}e^{-{\frac {\rho }{6}}}\sigma \upsilon \nu \theta }
6dz2 : n=6,
ℓ
{\displaystyle \ell }
ψ
(
r
,
θ
,
ϕ
)
=
1
839.808
21
π
r
2
(
9.072
−
1.512
ρ
+
72
ρ
2
−
ρ
3
)
e
−
ρ
6
(
3
σ
υ
ν
2
θ
−
1
)
{\displaystyle \psi {\begin{pmatrix}r,\theta ,\phi \end{pmatrix}}={\frac {1}{839.808{\sqrt {21\pi }}}}r^{2}{\begin{pmatrix}9.072-1.512\rho +72\rho ^{2}-\rho ^{3}\end{pmatrix}}e^{-{\frac {\rho }{6}}}{\begin{pmatrix}3\sigma \upsilon \nu ^{2}\theta -1\end{pmatrix}}}
6dzx : n=6,
ℓ
{\displaystyle \ell }
ψ
(
r
,
θ
,
ϕ
)
=
1
419.904
35
π
r
2
(
9.072
−
1.512
ρ
+
72
ρ
2
−
ρ
3
)
e
−
ρ
6
η
μ
θ
σ
υ
ν
θ
σ
υ
ν
ϕ
{\displaystyle \psi {\begin{pmatrix}r,\theta ,\phi \end{pmatrix}}={\frac {1}{419.904{\sqrt {35\pi }}}}r^{2}{\begin{pmatrix}9.072-1.512\rho +72\rho ^{2}-\rho ^{3}\end{pmatrix}}e^{-{\frac {\rho }{6}}}\eta \mu \theta \sigma \upsilon \nu \theta \sigma \upsilon \nu \phi }
6dyz : n=6,
ℓ
{\displaystyle \ell }
ψ
(
r
,
θ
,
ϕ
)
=
1
419.904
35
π
r
2
(
9.072
−
1.512
ρ
+
72
ρ
2
−
ρ
3
)
e
−
ρ
6
η
μ
θ
σ
υ
ν
θ
η
μ
ϕ
{\displaystyle \psi {\begin{pmatrix}r,\theta ,\phi \end{pmatrix}}={\frac {1}{419.904{\sqrt {35\pi }}}}r^{2}{\begin{pmatrix}9.072-1.512\rho +72\rho ^{2}-\rho ^{3}\end{pmatrix}}e^{-{\frac {\rho }{6}}}\eta \mu \theta \sigma \upsilon \nu \theta \eta \mu \phi }
6dx2 -y2 : n=6,
ℓ
{\displaystyle \ell }
ψ
(
r
,
θ
,
ϕ
)
=
1
839.808
35
π
r
2
(
9.072
−
1.512
ρ
+
72
ρ
2
−
ρ
3
)
e
−
ρ
6
η
μ
2
θ
σ
υ
ν
(
2
ϕ
)
{\displaystyle \psi {\begin{pmatrix}r,\theta ,\phi \end{pmatrix}}={\frac {1}{839.808{\sqrt {35\pi }}}}r^{2}{\begin{pmatrix}9.072-1.512\rho +72\rho ^{2}-\rho ^{3}\end{pmatrix}}e^{-{\frac {\rho }{6}}}\eta \mu ^{2}\theta \sigma \upsilon \nu {\begin{pmatrix}2\phi \end{pmatrix}}}
6dxy : n=6,
ℓ
{\displaystyle \ell }
ψ
(
r
,
θ
,
ϕ
)
=
1
419.904
35
π
r
2
(
9.072
−
1.512
ρ
+
72
ρ
2
−
ρ
3
)
e
−
ρ
6
(
5
η
μ
2
θ
σ
υ
ν
2
ϕ
−
3
)
η
μ
θ
σ
υ
ν
ϕ
{\displaystyle \psi {\begin{pmatrix}r,\theta ,\phi \end{pmatrix}}={\frac {1}{419.904{\sqrt {35\pi }}}}r^{2}{\begin{pmatrix}9.072-1.512\rho +72\rho ^{2}-\rho ^{3}\end{pmatrix}}e^{-{\frac {\rho }{6}}}{\begin{pmatrix}5\eta \mu ^{2}\theta \sigma \upsilon \nu ^{2}\phi -3\end{pmatrix}}\eta \mu \theta \sigma \upsilon \nu \phi }
6fx3 : n=6,
ℓ
{\displaystyle \ell }
ψ
(
r
,
θ
,
ϕ
)
=
1
97.200
10
π
r
3
(
24
−
ρ
)
e
−
ρ
6
(
5
η
μ
2
θ
σ
υ
ν
2
ϕ
−
3
)
η
μ
θ
σ
υ
ν
ϕ
{\displaystyle \psi {\begin{pmatrix}r,\theta ,\phi \end{pmatrix}}={\frac {1}{97.200{\sqrt {10\pi }}}}r^{3}{\begin{pmatrix}24-\rho \end{pmatrix}}e^{-{\frac {\rho }{6}}}{\begin{pmatrix}5\eta \mu ^{2}\theta \sigma \upsilon \nu ^{2}\phi -3\end{pmatrix}}\eta \mu \theta \sigma \upsilon \nu \phi }
6fy3 : n=6,
ℓ
{\displaystyle \ell }
ψ
(
r
,
θ
,
ϕ
)
=
1
97.200
10
π
r
3
(
24
−
ρ
)
e
−
ρ
6
(
5
η
μ
2
θ
η
μ
2
ϕ
−
3
)
η
μ
θ
η
μ
ϕ
{\displaystyle \psi {\begin{pmatrix}r,\theta ,\phi \end{pmatrix}}={\frac {1}{97.200{\sqrt {10\pi }}}}r^{3}{\begin{pmatrix}24-\rho \end{pmatrix}}e^{-{\frac {\rho }{6}}}{\begin{pmatrix}5\eta \mu ^{2}\theta \eta \mu ^{2}\phi -3\end{pmatrix}}\eta \mu \theta \eta \mu \phi }
6fz3 : n=6,
ℓ
{\displaystyle \ell }
ψ
(
r
,
θ
,
ϕ
)
=
1
97.200
10
π
r
3
(
24
−
ρ
)
e
−
ρ
6
(
5
σ
υ
ν
2
θ
−
3
)
σ
υ
ν
θ
{\displaystyle \psi {\begin{pmatrix}r,\theta ,\phi \end{pmatrix}}={\frac {1}{97.200{\sqrt {10\pi }}}}r^{3}{\begin{pmatrix}24-\rho \end{pmatrix}}e^{-{\frac {\rho }{6}}}{\begin{pmatrix}5\sigma \upsilon \nu ^{2}\theta -3\end{pmatrix}}\sigma \upsilon \nu \theta }
6fx(z2 -y2 ) : n=6,
ℓ
{\displaystyle \ell }
ψ
(
r
,
θ
,
ϕ
)
=
3
97.200
2
π
r
3
(
24
−
ρ
)
e
−
ρ
6
(
σ
υ
ν
2
θ
−
η
μ
2
θ
η
μ
2
ϕ
)
η
μ
θ
σ
υ
ν
ϕ
{\displaystyle \psi {\begin{pmatrix}r,\theta ,\phi \end{pmatrix}}={\frac {\sqrt {3}}{97.200{\sqrt {2\pi }}}}r^{3}{\begin{pmatrix}24-\rho \end{pmatrix}}e^{-{\frac {\rho }{6}}}{\begin{pmatrix}\sigma \upsilon \nu ^{2}\theta -\eta \mu ^{2}\theta \eta \mu ^{2}\phi \end{pmatrix}}\eta \mu \theta \sigma \upsilon \nu \phi }
6fy(z2 -x2 ) : n=6,
ℓ
{\displaystyle \ell }
ψ
(
r
,
θ
,
ϕ
)
=
3
97.200
2
π
r
3
(
24
−
ρ
)
e
−
ρ
6
(
σ
υ
ν
2
θ
−
η
μ
2
θ
σ
υ
ν
2
ϕ
)
η
μ
θ
η
μ
ϕ
{\displaystyle \psi {\begin{pmatrix}r,\theta ,\phi \end{pmatrix}}={\frac {\sqrt {3}}{97.200{\sqrt {2\pi }}}}r^{3}{\begin{pmatrix}24-\rho \end{pmatrix}}e^{-{\frac {\rho }{6}}}{\begin{pmatrix}\sigma \upsilon \nu ^{2}\theta -\eta \mu ^{2}\theta \sigma \upsilon \nu ^{2}\phi \end{pmatrix}}\eta \mu \theta \eta \mu \phi }
6fz(x2 -y2 ) : n=6,
ℓ
{\displaystyle \ell }
ψ
(
r
,
θ
,
ϕ
)
=
3
97.200
2
π
r
3
(
24
−
ρ
)
e
−
ρ
6
(
1
−
2
η
μ
2
ϕ
)
σ
υ
ν
θ
η
μ
2
θ
{\displaystyle \psi {\begin{pmatrix}r,\theta ,\phi \end{pmatrix}}={\frac {\sqrt {3}}{97.200{\sqrt {2\pi }}}}r^{3}{\begin{pmatrix}24-\rho \end{pmatrix}}e^{-{\frac {\rho }{6}}}{\begin{pmatrix}1-2\eta \mu ^{2}\phi \end{pmatrix}}\sigma \upsilon \nu \theta \eta \mu ^{2}\theta }
6fxyz : n=6,
ℓ
{\displaystyle \ell }
ψ
(
r
,
θ
,
ϕ
)
=
3
194.400
2
π
r
3
(
24
−
ρ
)
e
−
ρ
6
σ
υ
ν
θ
η
μ
2
θ
σ
υ
ν
ϕ
η
μ
ϕ
{\displaystyle \psi {\begin{pmatrix}r,\theta ,\phi \end{pmatrix}}={\frac {\sqrt {3}}{194.400{\sqrt {2\pi }}}}r^{3}{\begin{pmatrix}24-\rho \end{pmatrix}}e^{-{\frac {\rho }{6}}}\sigma \upsilon \nu \theta \eta \mu ^{2}\theta \sigma \upsilon \nu \phi \eta \mu \phi }
6gz4 : n=6,
ℓ
{\displaystyle \ell }
ψ
(
r
,
θ
,
ϕ
)
=
k
457.400
70
π
r
4
(
24
−
ρ
)
e
−
ρ
6
(
35
σ
υ
ν
4
θ
−
30
σ
υ
ν
2
θ
+
3
)
{\displaystyle \psi {\begin{pmatrix}r,\theta ,\phi \end{pmatrix}}={\frac {k}{457.400{\sqrt {70\pi }}}}r^{4}{\begin{pmatrix}24-\rho \end{pmatrix}}e^{-{\frac {\rho }{6}}}{\begin{pmatrix}35\sigma \upsilon \nu ^{4}\theta -30\sigma \upsilon \nu ^{2}\theta +3\end{pmatrix}}}
6gz2 x : n=6,
ℓ
{\displaystyle \ell }
ψ
(
r
,
θ
,
ϕ
)
=
k
457.400
70
π
r
4
(
24
−
ρ
)
e
−
ρ
6
(
4
σ
υ
ν
2
θ
−
3
η
μ
2
θ
σ
υ
ν
2
ϕ
−
3
η
μ
2
θ
η
μ
2
ϕ
)
η
μ
θ
σ
υ
ν
ϕ
σ
υ
ν
θ
{\displaystyle \psi {\begin{pmatrix}r,\theta ,\phi \end{pmatrix}}={\frac {k}{457.400{\sqrt {70\pi }}}}r^{4}{\begin{pmatrix}24-\rho \end{pmatrix}}e^{-{\frac {\rho }{6}}}{\begin{pmatrix}4\sigma \upsilon \nu ^{2}\theta -3\eta \mu ^{2}\theta \sigma \upsilon \nu ^{2}\phi -3\eta \mu ^{2}\theta \eta \mu ^{2}\phi \end{pmatrix}}\eta \mu \theta \sigma \upsilon \nu \phi \sigma \upsilon \nu \theta }
6gz2 y : n=6,
ℓ
{\displaystyle \ell }
ψ
(
r
,
θ
,
ϕ
)
=
k
457.400
70
π
r
4
(
24
−
ρ
)
e
−
ρ
6
(
4
σ
υ
ν
2
θ
−
3
η
μ
2
θ
σ
υ
ν
2
ϕ
−
3
η
μ
2
θ
η
μ
2
ϕ
)
η
μ
θ
η
μ
ϕ
σ
υ
ν
θ
{\displaystyle \psi {\begin{pmatrix}r,\theta ,\phi \end{pmatrix}}={\frac {k}{457.400{\sqrt {70\pi }}}}r^{4}{\begin{pmatrix}24-\rho \end{pmatrix}}e^{-{\frac {\rho }{6}}}{\begin{pmatrix}4\sigma \upsilon \nu ^{2}\theta -3\eta \mu ^{2}\theta \sigma \upsilon \nu ^{2}\phi -3\eta \mu ^{2}\theta \eta \mu ^{2}\phi \end{pmatrix}}\eta \mu \theta \eta \mu \phi \sigma \upsilon \nu \theta }
6gz2 xy : n=6,
ℓ
{\displaystyle \ell }
ψ
(
r
,
θ
,
ϕ
)
=
k
457.400
70
π
r
4
(
24
−
ρ
)
e
−
ρ
6
(
6
σ
υ
ν
2
θ
−
η
μ
2
θ
σ
υ
ν
2
ϕ
−
η
μ
2
θ
η
μ
2
ϕ
)
η
μ
2
θ
η
μ
ϕ
σ
υ
ν
ϕ
{\displaystyle \psi {\begin{pmatrix}r,\theta ,\phi \end{pmatrix}}={\frac {k}{457.400{\sqrt {70\pi }}}}r^{4}{\begin{pmatrix}24-\rho \end{pmatrix}}e^{-{\frac {\rho }{6}}}{\begin{pmatrix}6\sigma \upsilon \nu ^{2}\theta -\eta \mu ^{2}\theta \sigma \upsilon \nu ^{2}\phi -\eta \mu ^{2}\theta \eta \mu ^{2}\phi \end{pmatrix}}\eta \mu ^{2}\theta \eta \mu \phi \sigma \upsilon \nu \phi }
6gz2 (x2 -y2 ) : n=6,
ℓ
{\displaystyle \ell }
ψ
(
r
,
θ
,
ϕ
)
=
k
457.400
70
π
r
4
(
24
−
ρ
)
e
−
ρ
6
(
6
σ
υ
ν
2
θ
−
η
μ
2
θ
σ
υ
ν
2
ϕ
−
η
μ
2
θ
η
μ
2
ϕ
)
(
1
−
2
η
μ
2
ϕ
)
η
μ
2
θ
{\displaystyle \psi {\begin{pmatrix}r,\theta ,\phi \end{pmatrix}}={\frac {k}{457.400{\sqrt {70\pi }}}}r^{4}{\begin{pmatrix}24-\rho \end{pmatrix}}e^{-{\frac {\rho }{6}}}{\begin{pmatrix}6\sigma \upsilon \nu ^{2}\theta -\eta \mu ^{2}\theta \sigma \upsilon \nu ^{2}\phi -\eta \mu ^{2}\theta \eta \mu ^{2}\phi \end{pmatrix}}{\begin{pmatrix}1-2\eta \mu ^{2}\phi \end{pmatrix}}\eta \mu ^{2}\theta }
6gzx3 : n=6,
ℓ
{\displaystyle \ell }
ψ
(
r
,
θ
,
ϕ
)
=
k
457.400
70
π
r
4
(
24
−
ρ
)
e
−
ρ
6
η
μ
3
θ
σ
υ
ν
ϕ
σ
υ
ν
θ
(
1
−
4
η
μ
2
ϕ
)
{\displaystyle \psi {\begin{pmatrix}r,\theta ,\phi \end{pmatrix}}={\frac {k}{457.400{\sqrt {70\pi }}}}r^{4}{\begin{pmatrix}24-\rho \end{pmatrix}}e^{-{\frac {\rho }{6}}}\eta \mu ^{3}\theta \sigma \upsilon \nu \phi \sigma \upsilon \nu \theta {\begin{pmatrix}1-4\eta \mu ^{2}\phi \end{pmatrix}}}
6gzy3 : n=6,
ℓ
{\displaystyle \ell }
ψ
(
r
,
θ
,
ϕ
)
=
k
457.400
70
π
r
4
(
24
−
ρ
)
e
−
ρ
6
η
μ
3
θ
η
μ
ϕ
σ
υ
ν
θ
(
3
−
4
η
μ
2
ϕ
)
{\displaystyle \psi {\begin{pmatrix}r,\theta ,\phi \end{pmatrix}}={\frac {k}{457.400{\sqrt {70\pi }}}}r^{4}{\begin{pmatrix}24-\rho \end{pmatrix}}e^{-{\frac {\rho }{6}}}\eta \mu ^{3}\theta \eta \mu \phi \sigma \upsilon \nu \theta {\begin{pmatrix}3-4\eta \mu ^{2}\phi \end{pmatrix}}}
6gxy(x2 -y2 ) : n=6,
ℓ
{\displaystyle \ell }
ψ
(
r
,
θ
,
ϕ
)
=
k
457.400
70
π
r
4
(
24
−
ρ
)
e
−
ρ
6
η
μ
3
θ
σ
υ
ν
ϕ
σ
υ
ν
θ
(
1
−
2
η
μ
2
ϕ
)
{\displaystyle \psi {\begin{pmatrix}r,\theta ,\phi \end{pmatrix}}={\frac {k}{457.400{\sqrt {70\pi }}}}r^{4}{\begin{pmatrix}24-\rho \end{pmatrix}}e^{-{\frac {\rho }{6}}}\eta \mu ^{3}\theta \sigma \upsilon \nu \phi \sigma \upsilon \nu \theta {\begin{pmatrix}1-2\eta \mu ^{2}\phi \end{pmatrix}}}
6gx4 +y4 : n=6,
ℓ
{\displaystyle \ell }
ψ
(
r
,
θ
,
ϕ
)
=
k
457.400
70
π
r
4
(
24
−
ρ
)
e
−
ρ
6
η
μ
4
θ
(
1
−
4
σ
υ
ν
2
ϕ
η
μ
2
ϕ
)
{\displaystyle \psi {\begin{pmatrix}r,\theta ,\phi \end{pmatrix}}={\frac {k}{457.400{\sqrt {70\pi }}}}r^{4}{\begin{pmatrix}24-\rho \end{pmatrix}}e^{-{\frac {\rho }{6}}}\eta \mu ^{4}\theta {\begin{pmatrix}1-4\sigma \upsilon \nu ^{2}\phi \eta \mu ^{2}\phi \end{pmatrix}}}
7s: n=7,
ℓ
{\displaystyle \ell }
ψ
(
r
,
θ
,
ϕ
)
=
1
117.649
k
π
(
296.475.480
−
254.121.408
ρ
+
60.505.200
ρ
2
−
5.762.400
ρ
3
+
246.960
ρ
4
−
4.704
ρ
5
+
32
ρ
6
)
e
−
ρ
7
{\displaystyle \psi {\begin{pmatrix}r,\theta ,\phi \end{pmatrix}}={\frac {1}{117.649k{\sqrt {\pi }}}}{\begin{pmatrix}296.475.480-254.121.408\rho +60.505.200\rho ^{2}-5.762.400\rho ^{3}+246.960\rho ^{4}-4.704\rho ^{5}+32\rho ^{6}\end{pmatrix}}e^{-{\frac {\rho }{7}}}}
7px : n=7,
ℓ
{\displaystyle \ell }
ψ
(
r
,
θ
,
ϕ
)
=
3
117.649
k
π
r
(
112.943.040
−
40.336.800
ρ
+
4.609.920
ρ
2
−
164.640
ρ
3
+
4.480
ρ
4
−
32
ρ
5
)
e
−
ρ
7
η
μ
θ
σ
υ
ν
ϕ
{\displaystyle \psi {\begin{pmatrix}r,\theta ,\phi \end{pmatrix}}={\frac {\sqrt {3}}{117.649k{\sqrt {\pi }}}}r{\begin{pmatrix}112.943.040-40.336.800\rho +4.609.920\rho ^{2}-164.640\rho ^{3}+4.480\rho ^{4}-32\rho ^{5}\end{pmatrix}}e^{-{\frac {\rho }{7}}}\eta \mu \theta \sigma \upsilon \nu \phi }
7py : n=7,
ℓ
{\displaystyle \ell }
ψ
(
r
,
θ
,
ϕ
)
=
3
117.649
k
π
r
(
112.943.040
−
40.336.800
ρ
+
4.609.920
ρ
2
−
164.640
ρ
3
+
4.480
ρ
4
−
32
ρ
5
)
e
−
ρ
7
η
μ
θ
η
μ
ϕ
{\displaystyle \psi {\begin{pmatrix}r,\theta ,\phi \end{pmatrix}}={\frac {\sqrt {3}}{117.649k{\sqrt {\pi }}}}r{\begin{pmatrix}112.943.040-40.336.800\rho +4.609.920\rho ^{2}-164.640\rho ^{3}+4.480\rho ^{4}-32\rho ^{5}\end{pmatrix}}e^{-{\frac {\rho }{7}}}\eta \mu \theta \eta \mu \phi }
7pz : n=7,
ℓ
{\displaystyle \ell }
ψ
(
r
,
θ
,
ϕ
)
=
3
117.649
k
π
r
(
112.943.040
−
40.336.800
ρ
+
4.609.920
ρ
2
−
164.640
ρ
3
+
4.480
ρ
4
−
32
ρ
5
)
e
−
ρ
7
σ
υ
ν
θ
{\displaystyle \psi {\begin{pmatrix}r,\theta ,\phi \end{pmatrix}}={\frac {\sqrt {3}}{117.649k{\sqrt {\pi }}}}r{\begin{pmatrix}112.943.040-40.336.800\rho +4.609.920\rho ^{2}-164.640\rho ^{3}+4.480\rho ^{4}-32\rho ^{5}\end{pmatrix}}e^{-{\frac {\rho }{7}}}\sigma \upsilon \nu \theta }
7dz2 : n=7,
ℓ
{\displaystyle \ell }
ψ
(
r
,
θ
,
ϕ
)
=
1
453.789
21
π
r
2
(
14.406
−
2.958
ρ
+
84
ρ
2
−
ρ
3
)
e
−
ρ
7
(
3
σ
υ
ν
2
θ
−
1
)
{\displaystyle \psi {\begin{pmatrix}r,\theta ,\phi \end{pmatrix}}={\frac {1}{453.789{\sqrt {21\pi }}}}r^{2}{\begin{pmatrix}14.406-2.958\rho +84\rho ^{2}-\rho ^{3}\end{pmatrix}}e^{-{\frac {\rho }{7}}}{\begin{pmatrix}3\sigma \upsilon \nu ^{2}\theta -1\end{pmatrix}}}
7dzx : n=7,
ℓ
{\displaystyle \ell }
ψ
(
r
,
θ
,
ϕ
)
=
1
453.789
7
π
r
2
(
14.406
−
2.958
ρ
+
84
ρ
2
−
ρ
3
)
e
−
ρ
7
η
μ
θ
σ
υ
ν
θ
σ
υ
ν
ϕ
{\displaystyle \psi {\begin{pmatrix}r,\theta ,\phi \end{pmatrix}}={\frac {1}{453.789{\sqrt {7\pi }}}}r^{2}{\begin{pmatrix}14.406-2.958\rho +84\rho ^{2}-\rho ^{3}\end{pmatrix}}e^{-{\frac {\rho }{7}}}\eta \mu \theta \sigma \upsilon \nu \theta \sigma \upsilon \nu \phi }
7dyz : n=7,
ℓ
{\displaystyle \ell }
ψ
(
r
,
θ
,
ϕ
)
=
1
453.789
7
π
r
2
(
14.406
−
2.958
ρ
+
84
ρ
2
−
ρ
3
)
e
−
ρ
7
η
μ
θ
σ
υ
ν
θ
η
μ
ϕ
{\displaystyle \psi {\begin{pmatrix}r,\theta ,\phi \end{pmatrix}}={\frac {1}{453.789{\sqrt {7\pi }}}}r^{2}{\begin{pmatrix}14.406-2.958\rho +84\rho ^{2}-\rho ^{3}\end{pmatrix}}e^{-{\frac {\rho }{7}}}\eta \mu \theta \sigma \upsilon \nu \theta \eta \mu \phi }
7dx2 -y2 : n=7,
ℓ
{\displaystyle \ell }
ψ
(
r
,
θ
,
ϕ
)
=
1
907.578
7
π
r
2
(
14.406
−
2.958
ρ
+
84
ρ
2
−
ρ
3
)
e
−
ρ
7
η
μ
2
θ
σ
υ
ν
(
2
ϕ
)
{\displaystyle \psi {\begin{pmatrix}r,\theta ,\phi \end{pmatrix}}={\frac {1}{907.578{\sqrt {7\pi }}}}r^{2}{\begin{pmatrix}14.406-2.958\rho +84\rho ^{2}-\rho ^{3}\end{pmatrix}}e^{-{\frac {\rho }{7}}}\eta \mu ^{2}\theta \sigma \upsilon \nu {\begin{pmatrix}2\phi \end{pmatrix}}}
7dxy : n=7,
ℓ
{\displaystyle \ell }
ψ
(
r
,
θ
,
ϕ
)
=
1
453.789
7
π
r
2
(
14.406
−
2.958
ρ
+
84
ρ
2
−
ρ
3
)
e
−
ρ
7
(
5
η
μ
2
θ
σ
υ
ν
2
ϕ
−
3
)
η
μ
θ
σ
υ
ν
ϕ
{\displaystyle \psi {\begin{pmatrix}r,\theta ,\phi \end{pmatrix}}={\frac {1}{453.789{\sqrt {7\pi }}}}r^{2}{\begin{pmatrix}14.406-2.958\rho +84\rho ^{2}-\rho ^{3}\end{pmatrix}}e^{-{\frac {\rho }{7}}}{\begin{pmatrix}5\eta \mu ^{2}\theta \sigma \upsilon \nu ^{2}\phi -3\end{pmatrix}}\eta \mu \theta \sigma \upsilon \nu \phi }
7fx3 : n=7,
ℓ
{\displaystyle \ell }
ψ
(
r
,
θ
,
ϕ
)
=
1
180.075
10
π
r
3
(
28
−
ρ
)
e
−
ρ
7
(
5
η
μ
2
θ
σ
υ
ν
2
ϕ
−
3
)
η
μ
θ
σ
υ
ν
ϕ
{\displaystyle \psi {\begin{pmatrix}r,\theta ,\phi \end{pmatrix}}={\frac {1}{180.075{\sqrt {10\pi }}}}r^{3}{\begin{pmatrix}28-\rho \end{pmatrix}}e^{-{\frac {\rho }{7}}}{\begin{pmatrix}5\eta \mu ^{2}\theta \sigma \upsilon \nu ^{2}\phi -3\end{pmatrix}}\eta \mu \theta \sigma \upsilon \nu \phi }
7fy3 : n=7,
ℓ
{\displaystyle \ell }
ψ
(
r
,
θ
,
ϕ
)
=
1
180.075
10
π
r
3
(
28
−
ρ
)
e
−
ρ
7
(
5
η
μ
2
θ
η
μ
2
ϕ
−
3
)
η
μ
θ
η
μ
ϕ
{\displaystyle \psi {\begin{pmatrix}r,\theta ,\phi \end{pmatrix}}={\frac {1}{180.075{\sqrt {10\pi }}}}r^{3}{\begin{pmatrix}28-\rho \end{pmatrix}}e^{-{\frac {\rho }{7}}}{\begin{pmatrix}5\eta \mu ^{2}\theta \eta \mu ^{2}\phi -3\end{pmatrix}}\eta \mu \theta \eta \mu \phi }
7fz3 : n=7,
ℓ
{\displaystyle \ell }
ψ
(
r
,
θ
,
ϕ
)
=
1
180.075
10
π
r
3
(
28
−
ρ
)
e
−
ρ
7
(
5
σ
υ
ν
2
θ
−
3
)
σ
υ
ν
θ
{\displaystyle \psi {\begin{pmatrix}r,\theta ,\phi \end{pmatrix}}={\frac {1}{180.075{\sqrt {10\pi }}}}r^{3}{\begin{pmatrix}28-\rho \end{pmatrix}}e^{-{\frac {\rho }{7}}}{\begin{pmatrix}5\sigma \upsilon \nu ^{2}\theta -3\end{pmatrix}}\sigma \upsilon \nu \theta }
7fx(z2 -y2 ) : n=7,
ℓ
{\displaystyle \ell }
ψ
(
r
,
θ
,
ϕ
)
=
3
180.075
2
π
r
3
(
28
−
ρ
)
e
−
ρ
7
(
σ
υ
ν
2
θ
−
η
μ
2
θ
η
μ
2
ϕ
)
η
μ
θ
σ
υ
ν
ϕ
{\displaystyle \psi {\begin{pmatrix}r,\theta ,\phi \end{pmatrix}}={\frac {\sqrt {3}}{180.075{\sqrt {2\pi }}}}r^{3}{\begin{pmatrix}28-\rho \end{pmatrix}}e^{-{\frac {\rho }{7}}}{\begin{pmatrix}\sigma \upsilon \nu ^{2}\theta -\eta \mu ^{2}\theta \eta \mu ^{2}\phi \end{pmatrix}}\eta \mu \theta \sigma \upsilon \nu \phi }
7fy(z2 -x2 ) : n=7,
ℓ
{\displaystyle \ell }
ψ
(
r
,
θ
,
ϕ
)
=
3
180.075
2
π
r
3
(
28
−
ρ
)
e
−
ρ
7
(
σ
υ
ν
2
θ
−
η
μ
2
θ
σ
υ
ν
2
ϕ
)
η
μ
θ
η
μ
ϕ
{\displaystyle \psi {\begin{pmatrix}r,\theta ,\phi \end{pmatrix}}={\frac {\sqrt {3}}{180.075{\sqrt {2\pi }}}}r^{3}{\begin{pmatrix}28-\rho \end{pmatrix}}e^{-{\frac {\rho }{7}}}{\begin{pmatrix}\sigma \upsilon \nu ^{2}\theta -\eta \mu ^{2}\theta \sigma \upsilon \nu ^{2}\phi \end{pmatrix}}\eta \mu \theta \eta \mu \phi }
7fz(x2 -y2 ) : n=7,
ℓ
{\displaystyle \ell }
ψ
(
r
,
θ
,
ϕ
)
=
3
180.075
2
π
r
3
(
28
−
ρ
)
e
−
ρ
7
(
1
−
2
η
μ
2
ϕ
)
σ
υ
ν
θ
η
μ
2
θ
{\displaystyle \psi {\begin{pmatrix}r,\theta ,\phi \end{pmatrix}}={\frac {\sqrt {3}}{180.075{\sqrt {2\pi }}}}r^{3}{\begin{pmatrix}28-\rho \end{pmatrix}}e^{-{\frac {\rho }{7}}}{\begin{pmatrix}1-2\eta \mu ^{2}\phi \end{pmatrix}}\sigma \upsilon \nu \theta \eta \mu ^{2}\theta }
7fxyz : n=7,
ℓ
{\displaystyle \ell }
ψ
(
r
,
θ
,
ϕ
)
=
3
360.150
2
π
r
3
(
28
−
ρ
)
e
−
ρ
7
σ
υ
ν
θ
η
μ
2
θ
σ
υ
ν
ϕ
η
μ
ϕ
{\displaystyle \psi {\begin{pmatrix}r,\theta ,\phi \end{pmatrix}}={\frac {\sqrt {3}}{360.150{\sqrt {2\pi }}}}r^{3}{\begin{pmatrix}28-\rho \end{pmatrix}}e^{-{\frac {\rho }{7}}}\sigma \upsilon \nu \theta \eta \mu ^{2}\theta \sigma \upsilon \nu \phi \eta \mu \phi }
