En este apartado se muestran todas las funciones hidrogenoides posibles para valores de n entre 1 y 5.
Ψ
100
(
r
,
θ
,
ϕ
)
=
1
π
(
Z
a
)
3
2
e
−
Z
r
a
{\displaystyle \Psi _{100}(r,\theta ,\phi )={\frac {1}{\sqrt {\pi }}}{\biggl (}{\frac {Z}{a}}{\biggr )}^{\frac {3}{2}}e^{-{\frac {Zr}{a}}}}
Ψ
200
(
r
,
θ
,
ϕ
)
=
1
π
(
Z
2
a
)
3
2
(
1
−
Z
r
2
a
)
e
−
Z
r
2
a
{\displaystyle \Psi _{200}(r,\theta ,\phi )={\frac {1}{\sqrt {\pi }}}\left({\frac {Z}{2a}}\right)^{\frac {3}{2}}{\biggl (}1-{\frac {Zr}{2a}}{\biggr )}e^{-{\frac {Zr}{2a}}}}
Ψ
21
−
1
(
r
,
θ
,
ϕ
)
=
1
8
π
(
Z
a
)
5
2
r
e
−
Z
r
2
a
s
i
n
θ
e
−
i
ϕ
{\displaystyle \Psi _{21-1}(r,\theta ,\phi )={\frac {1}{8{\sqrt {\pi }}}}\left({\frac {Z}{a}}\right)^{\frac {5}{2}}re^{-{\frac {Zr}{2a}}}sin\theta e^{-i\phi }}
Ψ
210
(
r
,
θ
,
ϕ
)
=
1
4
2
π
(
Z
a
)
5
2
r
e
−
Z
r
2
a
c
o
s
θ
{\displaystyle \Psi _{210}(r,\theta ,\phi )={\frac {1}{4{\sqrt {2\pi }}}}\left({\frac {Z}{a}}\right)^{\frac {5}{2}}re^{-{\frac {Zr}{2a}}}cos\theta }
Ψ
211
(
r
,
θ
,
ϕ
)
=
1
8
π
(
Z
a
)
5
2
r
e
−
Z
r
2
a
s
i
n
θ
e
i
ϕ
{\displaystyle \Psi _{211}(r,\theta ,\phi )={\frac {1}{8{\sqrt {\pi }}}}\left({\frac {Z}{a}}\right)^{\frac {5}{2}}re^{-{\frac {Zr}{2a}}}sin\theta e^{i\phi }}
Ψ
300
(
r
,
θ
,
ϕ
)
=
1
81
3
π
(
Z
a
)
3
2
[
27
−
18
Z
r
a
+
2
Z
2
r
2
a
2
]
e
−
Z
r
3
a
{\displaystyle \Psi _{300}(r,\theta ,\phi )={\frac {1}{81{\sqrt {3\pi }}}}\left({\frac {Z}{a}}\right)^{\frac {3}{2}}\left[27-18{\frac {Zr}{a}}+2{\frac {Z^{2}r^{2}}{a^{2}}}\right]e^{-{\frac {Zr}{3a}}}}
Ψ
31
−
1
(
r
,
θ
,
ϕ
)
=
1
81
π
(
Z
a
)
5
2
e
−
Z
r
3
a
r
(
6
−
Z
r
a
)
e
−
i
ϕ
s
i
n
θ
{\displaystyle \Psi _{31-1}(r,\theta ,\phi )={\frac {1}{81{\sqrt {\pi }}}}\left({\frac {Z}{a}}\right)^{\frac {5}{2}}e^{-{\frac {Zr}{3a}}}r{\biggl (}6-{\frac {Zr}{a}}{\biggr )}e^{-i\phi }sin\theta }
Ψ
310
(
r
,
θ
,
ϕ
)
=
1
81
2
π
(
Z
a
)
5
2
e
−
Z
r
3
a
r
(
6
−
Z
r
a
)
c
o
s
θ
{\displaystyle \Psi _{310}(r,\theta ,\phi )={\frac {1}{81}}{\sqrt {\frac {2}{\pi }}}\left({\frac {Z}{a}}\right)^{\frac {5}{2}}e^{-{\frac {Zr}{3a}}}r{\biggl (}6-{\frac {Zr}{a}}{\biggr )}cos\theta }
Ψ
311
(
r
,
θ
,
ϕ
)
=
1
81
π
(
Z
a
)
5
2
e
−
Z
r
3
a
r
(
6
−
Z
r
a
)
e
i
ϕ
s
i
n
θ
{\displaystyle \Psi _{311}(r,\theta ,\phi )={\frac {1}{81{\sqrt {\pi }}}}\left({\frac {Z}{a}}\right)^{\frac {5}{2}}e^{-{\frac {Zr}{3a}}}r{\biggl (}6-{\frac {Zr}{a}}{\biggr )}e^{i\phi }sin\theta }
Ψ
32
−
2
(
r
,
θ
,
ϕ
)
=
1
108
π
(
Z
a
)
7
2
e
−
Z
r
3
a
r
2
e
−
2
i
ϕ
s
e
n
2
θ
{\displaystyle \Psi _{32-2}(r,\theta ,\phi )={\frac {1}{108{\sqrt {\pi }}}}\left({\frac {Z}{a}}\right)^{\frac {7}{2}}e^{-{\frac {Zr}{3a}}}r^{2}e^{-2i\phi }sen^{2}\theta }
Ψ
32
−
1
(
r
,
θ
,
ϕ
)
=
1
54
π
(
Z
a
)
7
2
e
−
Z
r
3
a
r
2
e
−
i
ϕ
s
e
n
θ
c
o
s
θ
{\displaystyle \Psi _{32-1}(r,\theta ,\phi )={\frac {1}{54{\sqrt {\pi }}}}\left({\frac {Z}{a}}\right)^{\frac {7}{2}}e^{-{\frac {Zr}{3a}}}r^{2}e^{-i\phi }sen\theta cos\theta }
Ψ
320
(
r
,
θ
,
ϕ
)
=
1
54
6
π
(
Z
a
)
−
7
2
e
−
Z
r
3
a
r
2
(
3
c
o
s
2
θ
−
1
)
{\displaystyle \Psi _{320}(r,\theta ,\phi )={\frac {1}{54{\sqrt {6\pi }}}}\left({\frac {Z}{a}}\right)^{-{\frac {7}{2}}}e^{-{\frac {Zr}{3a}}}r^{2}(3cos^{2}\theta -1)}
Ψ
321
(
r
,
θ
,
ϕ
)
=
1
54
π
(
Z
a
)
7
2
e
−
Z
r
3
a
r
2
e
i
ϕ
s
e
n
θ
c
o
s
θ
{\displaystyle \Psi _{321}(r,\theta ,\phi )={\frac {1}{54{\sqrt {\pi }}}}\left({\frac {Z}{a}}\right)^{\frac {7}{2}}e^{-{\frac {Zr}{3a}}}r^{2}e^{i\phi }sen\theta cos\theta }
Ψ
322
(
r
,
θ
,
ϕ
)
=
1
108
π
(
Z
a
)
7
2
e
−
Z
r
3
a
r
2
e
2
i
ϕ
s
e
n
2
θ
{\displaystyle \Psi _{322}(r,\theta ,\phi )={\frac {1}{108{\sqrt {\pi }}}}\left({\frac {Z}{a}}\right)^{\frac {7}{2}}e^{-{\frac {Zr}{3a}}}r^{2}e^{2i\phi }sen^{2}\theta }
Ψ
400
(
r
,
θ
,
ϕ
)
=
1
1536
π
(
Z
a
)
3
2
e
−
Z
r
4
a
[
192
−
144
Z
r
a
+
24
Z
2
r
2
a
2
−
Z
3
r
3
a
3
]
{\displaystyle \Psi _{400}(r,\theta ,\phi )={\frac {1}{1536{\sqrt {\pi }}}}\left({\frac {Z}{a}}\right)^{\frac {3}{2}}e^{-{\frac {Zr}{4a}}}\left[192-144{\frac {Zr}{a}}+24{\frac {Z^{2}r^{2}}{a^{2}}}-{\frac {Z^{3}r^{3}}{a^{3}}}\right]}
Ψ
41
−
1
=
1
512
5
π
e
−
Z
r
4
a
r
[
80
−
20
Z
r
a
+
Z
2
r
2
a
2
]
e
−
i
ϕ
s
i
n
θ
{\displaystyle \Psi _{41-1}={\frac {1}{512{\sqrt {5\pi }}}}e^{-{\frac {Zr}{4a}}}r\left[80-20{\frac {Zr}{a}}+{\frac {Z^{2}r^{2}}{a^{2}}}\right]e^{-i\phi }sin\theta }
Ψ
410
(
r
,
θ
,
ϕ
)
=
1
256
10
π
e
−
Z
r
4
a
r
[
80
−
20
Z
r
a
+
Z
2
r
2
a
2
]
c
o
s
θ
{\displaystyle \Psi _{410}(r,\theta ,\phi )={\frac {1}{256{\sqrt {10\pi }}}}e^{-{\frac {Zr}{4a}}}r\left[80-20{\frac {Zr}{a}}+{\frac {Z^{2}r^{2}}{a^{2}}}\right]cos\theta }
Ψ
411
=
1
512
5
π
e
−
Z
r
4
a
r
[
80
−
20
Z
r
a
+
Z
2
r
2
a
2
]
e
i
ϕ
s
i
n
θ
{\displaystyle \Psi _{411}={\frac {1}{512{\sqrt {5\pi }}}}e^{-{\frac {Zr}{4a}}}r\left[80-20{\frac {Zr}{a}}+{\frac {Z^{2}r^{2}}{a^{2}}}\right]e^{i\phi }sin\theta }
Ψ
42
−
2
(
r
,
θ
,
ϕ
)
=
1
1536
3
2
π
(
Z
a
)
7
2
e
−
Z
r
4
a
r
2
[
12
−
Z
r
a
]
e
−
2
i
ϕ
s
e
n
2
θ
{\displaystyle \Psi _{42-2}(r,\theta ,\phi )={\frac {1}{1536}}{\sqrt {\frac {3}{2\pi }}}\left({\frac {Z}{a}}\right)^{\frac {7}{2}}e^{-{\frac {Zr}{4a}}}r^{2}\left[12-{\frac {Zr}{a}}\right]e^{-2i\phi }sen^{2}\theta }
Ψ
42
−
1
(
r
,
θ
,
ϕ
)
=
1
768
3
2
π
(
Z
a
)
7
2
e
−
Z
r
4
a
r
2
[
12
−
Z
r
a
]
e
−
i
ϕ
s
e
n
θ
c
o
s
θ
{\displaystyle \Psi _{42-1}(r,\theta ,\phi )={\frac {1}{768}}{\sqrt {\frac {3}{2\pi }}}\left({\frac {Z}{a}}\right)^{\frac {7}{2}}e^{-{\frac {Zr}{4a}}}r^{2}\left[12-{\frac {Zr}{a}}\right]e^{-i\phi }sen\theta cos\theta }
Ψ
420
(
r
,
θ
,
ϕ
)
=
1
1536
π
(
Z
a
)
7
2
e
−
Z
r
4
a
r
2
[
12
−
Z
r
a
]
(
3
c
o
s
2
θ
−
1
)
{\displaystyle \Psi _{420}(r,\theta ,\phi )={\frac {1}{1536{\sqrt {\pi }}}}\left({\frac {Z}{a}}\right)^{\frac {7}{2}}e^{-{\frac {Zr}{4a}}}r^{2}\left[12-{\frac {Zr}{a}}\right]{\biggl (}3cos^{2}\theta -1{\biggr )}}
Ψ
421
(
r
,
θ
,
ϕ
)
=
1
768
3
2
π
(
Z
a
)
7
2
e
−
Z
r
4
a
r
2
[
12
−
Z
r
a
]
e
i
ϕ
s
e
n
θ
c
o
s
θ
{\displaystyle \Psi _{421}(r,\theta ,\phi )={\frac {1}{768}}{\sqrt {\frac {3}{2\pi }}}\left({\frac {Z}{a}}\right)^{\frac {7}{2}}e^{-{\frac {Zr}{4a}}}r^{2}\left[12-{\frac {Zr}{a}}\right]e^{i\phi }sen\theta cos\theta }
Ψ
422
(
r
,
θ
,
ϕ
)
=
1
1536
3
2
π
(
Z
a
)
7
2
e
−
Z
r
4
a
r
2
[
12
−
Z
r
a
]
e
2
i
ϕ
s
e
n
2
θ
{\displaystyle \Psi _{422}(r,\theta ,\phi )={\frac {1}{1536}}{\sqrt {\frac {3}{2\pi }}}\left({\frac {Z}{a}}\right)^{\frac {7}{2}}e^{-{\frac {Zr}{4a}}}r^{2}\left[12-{\frac {Zr}{a}}\right]e^{2i\phi }sen^{2}\theta }
Ψ
43
−
3
(
r
,
θ
,
ϕ
)
=
1
1536
2
π
(
Z
a
)
9
2
e
−
Z
r
4
a
r
3
e
−
3
i
ϕ
s
i
n
3
θ
{\displaystyle \Psi _{43-3}(r,\theta ,\phi )={\frac {1}{1536{\sqrt {2\pi }}}}\left({\frac {Z}{a}}\right)^{\frac {9}{2}}e^{-{\frac {Zr}{4a}}}r^{3}e^{-3i\phi }sin^{3}\theta }
Ψ
43
−
2
(
r
,
θ
,
ϕ
)
=
1
1536
3
π
(
Z
a
)
9
2
e
−
Z
r
4
a
r
3
e
−
2
i
ϕ
s
e
n
2
θ
c
o
s
θ
{\displaystyle \Psi _{43-2}(r,\theta ,\phi )={\frac {1}{1536}}{\sqrt {\frac {3}{\pi }}}\left({\frac {Z}{a}}\right)^{\frac {9}{2}}e^{-{\frac {Zr}{4a}}}r^{3}e^{-2i\phi }sen^{2}\theta cos\theta }
Ψ
43
−
1
(
r
,
θ
,
ϕ
)
=
1
1536
3
10
π
(
Z
a
)
9
2
e
−
Z
r
4
a
r
3
e
−
i
ϕ
s
i
n
θ
(
5
c
o
s
2
θ
−
1
)
{\displaystyle \Psi _{43-1}(r,\theta ,\phi )={\frac {1}{1536}}{\sqrt {\frac {3}{10\pi }}}\left({\frac {Z}{a}}\right)^{\frac {9}{2}}e^{-{\frac {Zr}{4a}}}r^{3}e^{-i\phi }sin\theta {\biggl (}5cos^{2}\theta -1{\biggr )}}
Ψ
430
(
r
,
θ
,
ϕ
)
=
1
768
10
π
(
Z
a
)
9
2
e
−
Z
r
4
a
r
3
(
5
c
o
s
3
θ
−
3
c
o
s
θ
)
{\displaystyle \Psi _{430}(r,\theta ,\phi )={\frac {1}{768{\sqrt {10\pi }}}}\left({\frac {Z}{a}}\right)^{\frac {9}{2}}e^{-{\frac {Zr}{4a}}}r^{3}{\biggl (}5cos^{3}\theta -3cos\theta {\biggr )}}
Ψ
431
(
r
,
θ
,
ϕ
)
=
1
1536
3
10
π
(
Z
a
)
9
2
e
−
Z
r
4
a
r
3
e
i
ϕ
s
i
n
θ
(
5
c
o
s
2
θ
−
1
)
{\displaystyle \Psi _{431}(r,\theta ,\phi )={\frac {1}{1536}}{\sqrt {\frac {3}{10\pi }}}\left({\frac {Z}{a}}\right)^{\frac {9}{2}}e^{-{\frac {Zr}{4a}}}r^{3}e^{i\phi }sin\theta {\biggl (}5cos^{2}\theta -1{\biggr )}}
Ψ
432
(
r
,
θ
,
ϕ
)
=
1
1536
3
π
(
Z
a
)
9
2
e
−
Z
r
4
a
r
3
e
2
i
ϕ
s
e
n
2
θ
c
o
s
θ
{\displaystyle \Psi _{432}(r,\theta ,\phi )={\frac {1}{1536}}{\sqrt {\frac {3}{\pi }}}\left({\frac {Z}{a}}\right)^{\frac {9}{2}}e^{-{\frac {Zr}{4a}}}r^{3}e^{2i\phi }sen^{2}\theta cos\theta }
Ψ
433
(
r
,
θ
,
ϕ
)
=
1
1536
2
π
(
Z
a
)
9
2
e
−
Z
r
4
a
r
3
e
3
i
ϕ
s
i
n
3
θ
{\displaystyle \Psi _{433}(r,\theta ,\phi )={\frac {1}{1536{\sqrt {2\pi }}}}\left({\frac {Z}{a}}\right)^{\frac {9}{2}}e^{-{\frac {Zr}{4a}}}r^{3}e^{3i\phi }sin^{3}\theta }
Ψ
500
(
r
,
θ
,
ϕ
)
=
1
46875
5
π
(
Z
a
)
3
2
e
−
Z
r
5
a
[
9375
−
7500
Z
r
5
a
+
1500
Z
2
r
2
a
2
−
100
Z
3
r
3
a
3
+
2
Z
4
r
4
a
4
]
{\displaystyle \Psi _{500}(r,\theta ,\phi )={\frac {1}{46875{\sqrt {5\pi }}}}\left({\frac {Z}{a}}\right)^{\frac {3}{2}}e^{-{\frac {Zr}{5a}}}\left[9375-7500{\frac {Zr}{5a}}+1500{\frac {Z^{2}r^{2}}{a^{2}}}-100{\frac {Z^{3}r^{3}}{a^{3}}}+2{\frac {Z^{4}r^{4}}{a^{4}}}\right]}
Ψ
51
−
1
(
r
,
θ
,
ϕ
)
=
1
46875
5
π
(
Z
a
)
5
2
e
−
Z
r
5
a
r
[
3750
−
1125
Z
r
a
+
90
Z
2
r
2
a
2
−
2
Z
3
r
3
a
3
]
e
−
i
ϕ
s
e
n
θ
{\displaystyle \Psi _{51-1}(r,\theta ,\phi )={\frac {1}{46875{\sqrt {5\pi }}}}\left({\frac {Z}{a}}\right)^{\frac {5}{2}}e^{-{\frac {Zr}{5a}}}r\left[3750-1125{\frac {Zr}{a}}+90{\frac {Z^{2}r^{2}}{a^{2}}}-2{\frac {Z^{3}r^{3}}{a^{3}}}\right]e^{-i\phi }sen\theta }
Ψ
510
(
r
,
θ
,
ϕ
)
=
1
46875
2
5
π
(
Z
a
)
5
2
e
−
Z
r
5
a
r
[
3750
−
1125
Z
r
a
+
90
Z
2
r
2
a
2
−
2
Z
3
r
3
a
3
]
c
o
s
θ
{\displaystyle \Psi _{510}(r,\theta ,\phi )={\frac {1}{46875}}{\sqrt {\frac {2}{5\pi }}}\left({\frac {Z}{a}}\right)^{\frac {5}{2}}e^{-{\frac {Zr}{5a}}}r\left[3750-1125{\frac {Zr}{a}}+90{\frac {Z^{2}r^{2}}{a^{2}}}-2{\frac {Z^{3}r^{3}}{a^{3}}}\right]cos\theta }
Ψ
511
(
r
,
θ
,
ϕ
)
=
1
46875
5
π
(
Z
a
)
5
2
e
−
Z
r
5
a
r
[
3750
−
1125
Z
r
a
+
90
Z
2
r
2
a
2
−
2
Z
3
r
3
a
3
]
e
i
ϕ
s
e
n
θ
{\displaystyle \Psi _{511}(r,\theta ,\phi )={\frac {1}{46875{\sqrt {5\pi }}}}\left({\frac {Z}{a}}\right)^{\frac {5}{2}}e^{-{\frac {Zr}{5a}}}r\left[3750-1125{\frac {Zr}{a}}+90{\frac {Z^{2}r^{2}}{a^{2}}}-2{\frac {Z^{3}r^{3}}{a^{3}}}\right]e^{i\phi }sen\theta }
Ψ
52
−
2
(
r
,
θ
,
ϕ
)
=
1
187500
3
7
π
(
Z
a
)
7
2
e
−
Z
r
5
a
r
2
[
1050
−
70
Z
r
a
+
Z
2
r
2
a
2
]
e
−
2
i
ϕ
s
i
n
2
θ
{\displaystyle \Psi _{52-2}(r,\theta ,\phi )={\frac {1}{187500}}{\sqrt {\frac {3}{7\pi }}}\left({\frac {Z}{a}}\right)^{\frac {7}{2}}e^{-{\frac {Zr}{5a}}}r^{2}\left[1050-70{\frac {Zr}{a}}+{\frac {Z^{2}r^{2}}{a^{2}}}\right]e^{-2i\phi }sin^{2}\theta }
Ψ
52
−
1
(
r
,
θ
,
ϕ
)
=
1
93750
3
7
π
(
Z
a
)
7
2
e
−
Z
r
5
a
r
2
[
1050
−
70
Z
r
a
+
Z
2
r
2
a
2
]
e
−
i
ϕ
s
i
n
θ
c
o
s
θ
{\displaystyle \Psi _{52-1}(r,\theta ,\phi )={\frac {1}{93750}}{\sqrt {\frac {3}{7\pi }}}\left({\frac {Z}{a}}\right)^{\frac {7}{2}}e^{-{\frac {Zr}{5a}}}r^{2}\left[1050-70{\frac {Zr}{a}}+{\frac {Z^{2}r^{2}}{a^{2}}}\right]e^{-i\phi }sin\theta cos\theta }
Ψ
520
(
r
,
θ
,
ϕ
)
=
1
93750
1
14
π
(
Z
a
)
7
2
e
−
Z
r
5
a
r
2
[
1050
−
70
Z
r
a
+
Z
2
r
2
a
2
]
(
3
cos
2
θ
−
1
)
{\displaystyle \Psi _{520}(r,\theta ,\phi )={\frac {1}{93750}}{\sqrt {\frac {1}{14\pi }}}\left({\frac {Z}{a}}\right)^{\frac {7}{2}}e^{-{\frac {Zr}{5a}}}r^{2}\left[1050-70{\frac {Zr}{a}}+{\frac {Z^{2}r^{2}}{a^{2}}}\right]{\biggl (}3\cos ^{2}\theta -1{\biggr )}}
Ψ
521
(
r
,
θ
,
ϕ
)
=
1
93750
3
7
π
(
Z
a
)
7
2
e
−
Z
r
5
a
r
2
[
1050
−
70
Z
r
a
+
Z
2
r
2
a
2
]
e
i
ϕ
s
i
n
θ
c
o
s
θ
{\displaystyle \Psi _{521}(r,\theta ,\phi )={\frac {1}{93750}}{\sqrt {\frac {3}{7\pi }}}\left({\frac {Z}{a}}\right)^{\frac {7}{2}}e^{-{\frac {Zr}{5a}}}r^{2}\left[1050-70{\frac {Zr}{a}}+{\frac {Z^{2}r^{2}}{a^{2}}}\right]e^{i\phi }sin\theta cos\theta }
Ψ
522
(
r
,
θ
,
ϕ
)
=
1
187500
3
7
π
(
Z
a
)
7
2
e
−
Z
r
5
a
r
2
[
1050
−
70
Z
r
a
+
Z
2
r
2
a
2
]
e
2
i
ϕ
s
i
n
2
θ
{\displaystyle \Psi _{522}(r,\theta ,\phi )={\frac {1}{187500}}{\sqrt {\frac {3}{7\pi }}}\left({\frac {Z}{a}}\right)^{\frac {7}{2}}e^{-{\frac {Zr}{5a}}}r^{2}\left[1050-70{\frac {Zr}{a}}+{\frac {Z^{2}r^{2}}{a^{2}}}\right]e^{2i\phi }sin^{2}\theta }
Ψ
53
−
3
(
r
,
θ
,
ϕ
)
=
1
93750
2
π
(
Z
a
)
9
2
e
−
Z
r
5
a
r
3
(
20
−
Z
r
a
)
e
−
3
i
ϕ
s
i
n
3
θ
{\displaystyle \Psi _{53-3}(r,\theta ,\phi )={\frac {1}{93750{\sqrt {2\pi }}}}\left({\frac {Z}{a}}\right)^{\frac {9}{2}}e^{-{\frac {Zr}{5a}}}r^{3}{\biggl (}20-{\frac {Zr}{a}}{\biggr )}e^{-3i\phi }sin^{3}\theta }
Ψ
53
−
2
(
r
,
θ
,
ϕ
)
=
1
93750
3
π
(
Z
a
)
9
2
e
−
Z
r
5
a
r
3
(
20
−
Z
r
a
)
e
−
2
i
ϕ
s
i
n
2
θ
c
o
s
θ
{\displaystyle \Psi _{53-2}(r,\theta ,\phi )={\frac {1}{93750}}{\sqrt {\frac {3}{\pi }}}\left({\frac {Z}{a}}\right)^{\frac {9}{2}}e^{-{\frac {Zr}{5a}}}r^{3}{\biggl (}20-{\frac {Zr}{a}}{\biggr )}e^{-2i\phi }sin^{2}\theta cos\theta }
Ψ
53
−
1
(
r
,
θ
,
ϕ
)
=
1
93750
3
10
π
(
Z
a
)
9
2
e
−
Z
r
5
a
r
3
(
20
−
Z
r
a
)
e
−
i
ϕ
s
i
n
θ
(
5
cos
2
θ
−
1
)
{\displaystyle \Psi _{53-1}(r,\theta ,\phi )={\frac {1}{93750}}{\sqrt {\frac {3}{10\pi }}}\left({\frac {Z}{a}}\right)^{\frac {9}{2}}e^{-{\frac {Zr}{5a}}}r^{3}{\biggl (}20-{\frac {Zr}{a}}{\biggr )}e^{-i\phi }sin\theta {\biggl (}5\cos ^{2}\theta -1{\biggr )}}
Ψ
530
(
r
,
θ
,
ϕ
)
=
1
46875
10
π
(
Z
a
)
9
2
e
−
Z
r
5
a
r
3
(
20
−
Z
r
a
)
(
5
cos
3
θ
−
3
c
o
s
θ
)
{\displaystyle \Psi _{530}(r,\theta ,\phi )={\frac {1}{46875{\sqrt {10\pi }}}}\left({\frac {Z}{a}}\right)^{\frac {9}{2}}e^{-{\frac {Zr}{5a}}}r^{3}{\biggl (}20-{\frac {Zr}{a}}{\biggr )}{\biggl (}5\cos ^{3}\theta -3cos\theta {\biggr )}}
Ψ
531
(
r
,
θ
,
ϕ
)
=
1
93750
3
10
π
(
Z
a
)
9
2
e
−
Z
r
5
a
r
3
(
20
−
Z
r
a
)
e
i
ϕ
s
i
n
θ
(
5
cos
2
θ
−
1
)
{\displaystyle \Psi _{531}(r,\theta ,\phi )={\frac {1}{93750}}{\sqrt {\frac {3}{10\pi }}}\left({\frac {Z}{a}}\right)^{\frac {9}{2}}e^{-{\frac {Zr}{5a}}}r^{3}{\biggl (}20-{\frac {Zr}{a}}{\biggr )}e^{i\phi }sin\theta {\biggl (}5\cos ^{2}\theta -1{\biggr )}}
Ψ
532
(
r
,
θ
,
ϕ
)
=
1
93750
3
π
(
Z
a
)
9
2
e
−
Z
r
5
a
r
3
(
20
−
Z
r
a
)
e
2
i
ϕ
s
i
n
2
θ
c
o
s
θ
{\displaystyle \Psi _{532}(r,\theta ,\phi )={\frac {1}{93750}}{\sqrt {\frac {3}{\pi }}}\left({\frac {Z}{a}}\right)^{\frac {9}{2}}e^{-{\frac {Zr}{5a}}}r^{3}{\biggl (}20-{\frac {Zr}{a}}{\biggr )}e^{2i\phi }sin^{2}\theta cos\theta }
Ψ
533
(
r
,
θ
,
ϕ
)
=
1
93750
2
π
(
Z
a
)
9
2
e
−
Z
r
5
a
r
3
(
20
−
Z
r
a
)
e
3
i
ϕ
s
i
n
3
θ
{\displaystyle \Psi _{533}(r,\theta ,\phi )={\frac {1}{93750{\sqrt {2\pi }}}}\left({\frac {Z}{a}}\right)^{\frac {9}{2}}e^{-{\frac {Zr}{5a}}}r^{3}{\biggl (}20-{\frac {Zr}{a}}{\biggr )}e^{3i\phi }sin^{3}\theta }
Ψ
54
−
4
(
r
,
θ
,
ϕ
)
=
1
375000
π
(
Z
a
)
11
2
e
−
Z
r
5
a
r
4
e
−
4
i
ϕ
s
i
n
4
θ
{\displaystyle \Psi _{54-4}(r,\theta ,\phi )={\frac {1}{375000{\sqrt {\pi }}}}\left({\frac {Z}{a}}\right)^{\frac {11}{2}}e^{-{\frac {Zr}{5a}}}r^{4}e^{-4i\phi }sin^{4}\theta }
Ψ
54
−
3
(
r
,
θ
,
ϕ
)
=
1
93750
2
π
(
Z
a
)
11
2
e
−
Z
r
5
a
r
4
e
−
3
i
ϕ
s
i
n
3
θ
c
o
s
θ
{\displaystyle \Psi _{54-3}(r,\theta ,\phi )={\frac {1}{93750{\sqrt {2\pi }}}}\left({\frac {Z}{a}}\right)^{\frac {11}{2}}e^{-{\frac {Zr}{5a}}}r^{4}e^{-3i\phi }sin^{3}\theta cos\theta }
Ψ
54
−
2
(
r
,
θ
,
ϕ
)
=
1
187500
7
π
(
Z
a
)
11
2
e
−
Z
r
5
a
r
4
e
−
2
i
ϕ
s
i
n
2
θ
(
7
c
o
s
2
θ
−
1
)
{\displaystyle \Psi _{54-2}(r,\theta ,\phi )={\frac {1}{187500{\sqrt {7\pi }}}}\left({\frac {Z}{a}}\right)^{\frac {11}{2}}e^{-{\frac {Zr}{5a}}}r^{4}e^{-2i\phi }sin^{2}\theta {\biggl (}7cos^{2}\theta -1{\biggr )}}
Ψ
54
−
1
(
r
,
θ
,
ϕ
)
=
1
93750
14
π
(
Z
a
)
11
2
e
−
Z
r
5
a
r
4
e
−
i
ϕ
s
i
n
θ
(
7
c
o
s
3
θ
−
3
c
o
s
θ
)
{\displaystyle \Psi _{54-1}(r,\theta ,\phi )={\frac {1}{93750{\sqrt {14\pi }}}}\left({\frac {Z}{a}}\right)^{\frac {11}{2}}e^{-{\frac {Zr}{5a}}}r^{4}e^{-i\phi }sin\theta {\biggl (}7cos^{3}\theta -3cos\theta {\biggr )}}
Ψ
540
(
r
,
θ
,
ϕ
)
=
1
187500
70
π
(
Z
a
)
11
2
e
−
Z
r
5
a
r
4
(
35
c
o
s
4
θ
−
30
c
o
s
2
θ
+
3
)
{\displaystyle \Psi _{540}(r,\theta ,\phi )={\frac {1}{187500{\sqrt {70\pi }}}}\left({\frac {Z}{a}}\right)^{\frac {11}{2}}e^{-{\frac {Zr}{5a}}}r^{4}{\biggl (}35cos^{4}\theta -30cos^{2}\theta +3{\biggr )}}
Ψ
541
(
r
,
θ
,
ϕ
)
=
1
93750
14
π
(
Z
a
)
11
2
e
−
Z
r
5
a
r
4
e
i
ϕ
s
i
n
θ
(
7
c
o
s
3
θ
−
3
c
o
s
θ
)
{\displaystyle \Psi _{541}(r,\theta ,\phi )={\frac {1}{93750{\sqrt {14\pi }}}}\left({\frac {Z}{a}}\right)^{\frac {11}{2}}e^{-{\frac {Zr}{5a}}}r^{4}e^{i\phi }sin\theta {\biggl (}7cos^{3}\theta -3cos\theta {\biggr )}}
Ψ
542
(
r
,
θ
,
ϕ
)
=
1
187500
7
π
(
Z
a
)
11
2
e
−
Z
r
5
a
r
4
e
2
i
ϕ
s
i
n
2
θ
(
7
c
o
s
2
θ
−
1
)
{\displaystyle \Psi _{542}(r,\theta ,\phi )={\frac {1}{187500{\sqrt {7\pi }}}}\left({\frac {Z}{a}}\right)^{\frac {11}{2}}e^{-{\frac {Zr}{5a}}}r^{4}e^{2i\phi }sin^{2}\theta {\biggl (}7cos^{2}\theta -1{\biggr )}}
Ψ
543
(
r
,
θ
,
ϕ
)
=
1
93750
2
π
(
Z
a
)
11
2
e
−
Z
r
5
a
r
4
e
3
i
ϕ
s
i
n
3
θ
c
o
s
θ
{\displaystyle \Psi _{543}(r,\theta ,\phi )={\frac {1}{93750{\sqrt {2\pi }}}}\left({\frac {Z}{a}}\right)^{\frac {11}{2}}e^{-{\frac {Zr}{5a}}}r^{4}e^{3i\phi }sin^{3}\theta cos\theta }
Ψ
544
(
r
,
θ
,
ϕ
)
=
1
375000
π
(
Z
a
)
11
2
e
−
Z
r
5
a
r
4
e
4
i
ϕ
s
i
n
4
θ
{\displaystyle \Psi _{544}(r,\theta ,\phi )={\frac {1}{375000{\sqrt {\pi }}}}\left({\frac {Z}{a}}\right)^{\frac {11}{2}}e^{-{\frac {Zr}{5a}}}r^{4}e^{4i\phi }sin^{4}\theta }