Table of normalised hydrogen wavefunctions |Ψ_n,l,m⟩

ψ_1,0,0=	$\frac{Z^{\frac{3}{2}}}{\sqrt{π} a^{\frac{3}{2}} ⅇ^{\frac{Z r}{a}}}$
ψ_2,0,0=	$- \frac{\sqrt{2} Z^{\frac{5}{2}} r}{8 \sqrt{π} a^{\frac{5}{2}} ⅇ^{\frac{Z r}{2 a}}} + \frac{\sqrt{2} Z^{\frac{3}{2}}}{4 \sqrt{π} a^{\frac{3}{2}} ⅇ^{\frac{Z r}{2 a}}}$
ψ_2,1,-1=	$\frac{Z^{\frac{5}{2}} r sin θ}{8 \sqrt{π} a^{\frac{5}{2}} ⅇ^{ⅈ φ} ⅇ^{\frac{Z r}{2 a}}}$
ψ_2,1,0=	$\frac{\sqrt{2} Z^{\frac{5}{2}} r cos θ}{8 \sqrt{π} a^{\frac{5}{2}} ⅇ^{\frac{Z r}{2 a}}}$
ψ_2,1,1=	$- \frac{Z^{\frac{5}{2}} r ⅇ^{ⅈ φ} sin θ}{8 \sqrt{π} a^{\frac{5}{2}} ⅇ^{\frac{Z r}{2 a}}}$
ψ_3,0,0=	$\frac{2 \sqrt{3} Z^{\frac{7}{2}} r^{2}}{243 \sqrt{π} a^{\frac{7}{2}} ⅇ^{\frac{Z r}{3 a}}} - \frac{2 \sqrt{3} Z^{\frac{5}{2}} r}{27 \sqrt{π} a^{\frac{5}{2}} ⅇ^{\frac{Z r}{3 a}}} + \frac{\sqrt{3} Z^{\frac{3}{2}}}{9 \sqrt{π} a^{\frac{3}{2}} ⅇ^{\frac{Z r}{3 a}}}$
ψ_3,1,-1=	$- \frac{Z^{\frac{7}{2}} r^{2} sin θ}{81 \sqrt{π} a^{\frac{7}{2}} ⅇ^{ⅈ φ} ⅇ^{\frac{Z r}{3 a}}} + \frac{2 Z^{\frac{5}{2}} r sin θ}{27 \sqrt{π} a^{\frac{5}{2}} ⅇ^{ⅈ φ} ⅇ^{\frac{Z r}{3 a}}}$
ψ_3,1,0=	$- \frac{\sqrt{2} Z^{\frac{7}{2}} r^{2} cos θ}{81 \sqrt{π} a^{\frac{7}{2}} ⅇ^{\frac{Z r}{3 a}}} + \frac{2 \sqrt{2} Z^{\frac{5}{2}} r cos θ}{27 \sqrt{π} a^{\frac{5}{2}} ⅇ^{\frac{Z r}{3 a}}}$
ψ_3,1,1=	$\frac{Z^{\frac{7}{2}} r^{2} ⅇ^{ⅈ φ} sin θ}{81 \sqrt{π} a^{\frac{7}{2}} ⅇ^{\frac{Z r}{3 a}}} - \frac{2 Z^{\frac{5}{2}} r ⅇ^{ⅈ φ} sin θ}{27 \sqrt{π} a^{\frac{5}{2}} ⅇ^{\frac{Z r}{3 a}}}$
ψ_3,2,-2=	$\frac{Z^{\frac{7}{2}} r^{2} (- \frac{{cos}^{2} θ}{162 \sqrt{π} ⅇ^{2 ⅈ φ} ⅇ^{\frac{Z r}{3 a}}} + \frac{1}{162 \sqrt{π} ⅇ^{2 ⅈ φ} ⅇ^{\frac{Z r}{3 a}}})}{a^{\frac{7}{2}}}$
ψ_3,2,-1=	$\frac{Z^{\frac{7}{2}} r^{2} sin θ cos θ}{81 \sqrt{π} a^{\frac{7}{2}} ⅇ^{ⅈ φ} ⅇ^{\frac{Z r}{3 a}}}$
ψ_3,2,0=	$\frac{Z^{\frac{7}{2}} r^{2} (\frac{\sqrt{6} {cos}^{2} θ}{162 \sqrt{π} ⅇ^{\frac{Z r}{3 a}}} - \frac{\sqrt{6}}{486 \sqrt{π} ⅇ^{\frac{Z r}{3 a}}})}{a^{\frac{7}{2}}}$
ψ_3,2,1=	$- \frac{Z^{\frac{7}{2}} r^{2} ⅇ^{ⅈ φ} sin θ cos θ}{81 \sqrt{π} a^{\frac{7}{2}} ⅇ^{\frac{Z r}{3 a}}}$
ψ_3,2,2=	$\frac{Z^{\frac{7}{2}} r^{2} (- \frac{ⅇ^{2 ⅈ φ} {cos}^{2} θ}{162 \sqrt{π} ⅇ^{\frac{Z r}{3 a}}} + \frac{ⅇ^{2 ⅈ φ}}{162 \sqrt{π} ⅇ^{\frac{Z r}{3 a}}})}{a^{\frac{7}{2}}}$
ψ_4,0,0=	$- \frac{Z^{\frac{9}{2}} r^{3}}{1536 \sqrt{π} a^{\frac{9}{2}} ⅇ^{\frac{Z r}{4 a}}} + \frac{Z^{\frac{7}{2}} r^{2}}{64 \sqrt{π} a^{\frac{7}{2}} ⅇ^{\frac{Z r}{4 a}}} - \frac{3 Z^{\frac{5}{2}} r}{32 \sqrt{π} a^{\frac{5}{2}} ⅇ^{\frac{Z r}{4 a}}} + \frac{Z^{\frac{3}{2}}}{8 \sqrt{π} a^{\frac{3}{2}} ⅇ^{\frac{Z r}{4 a}}}$
ψ_4,1,-1=	$\frac{\sqrt{10} Z^{\frac{9}{2}} r^{3} sin θ}{5120 \sqrt{π} a^{\frac{9}{2}} ⅇ^{ⅈ φ} ⅇ^{\frac{Z r}{4 a}}} - \frac{\sqrt{10} Z^{\frac{7}{2}} r^{2} sin θ}{256 \sqrt{π} a^{\frac{7}{2}} ⅇ^{ⅈ φ} ⅇ^{\frac{Z r}{4 a}}} + \frac{\sqrt{10} Z^{\frac{5}{2}} r sin θ}{64 \sqrt{π} a^{\frac{5}{2}} ⅇ^{ⅈ φ} ⅇ^{\frac{Z r}{4 a}}}$
ψ_4,1,0=	$\frac{\sqrt{5} Z^{\frac{9}{2}} r^{3} cos θ}{2560 \sqrt{π} a^{\frac{9}{2}} ⅇ^{\frac{Z r}{4 a}}} - \frac{\sqrt{5} Z^{\frac{7}{2}} r^{2} cos θ}{128 \sqrt{π} a^{\frac{7}{2}} ⅇ^{\frac{Z r}{4 a}}} + \frac{\sqrt{5} Z^{\frac{5}{2}} r cos θ}{32 \sqrt{π} a^{\frac{5}{2}} ⅇ^{\frac{Z r}{4 a}}}$
ψ_4,1,1=	$- \frac{\sqrt{10} Z^{\frac{9}{2}} r^{3} ⅇ^{ⅈ φ} sin θ}{5120 \sqrt{π} a^{\frac{9}{2}} ⅇ^{\frac{Z r}{4 a}}} + \frac{\sqrt{10} Z^{\frac{7}{2}} r^{2} ⅇ^{ⅈ φ} sin θ}{256 \sqrt{π} a^{\frac{7}{2}} ⅇ^{\frac{Z r}{4 a}}} - \frac{\sqrt{10} Z^{\frac{5}{2}} r ⅇ^{ⅈ φ} sin θ}{64 \sqrt{π} a^{\frac{5}{2}} ⅇ^{\frac{Z r}{4 a}}}$
ψ_4,2,-2=	$\frac{Z^{\frac{9}{2}} r^{3} (\frac{\sqrt{6} {cos}^{2} θ}{6144 \sqrt{π} ⅇ^{2 ⅈ φ} ⅇ^{\frac{Z r}{4 a}}} - \frac{\sqrt{6}}{6144 \sqrt{π} ⅇ^{2 ⅈ φ} ⅇ^{\frac{Z r}{4 a}}})}{a^{\frac{9}{2}}} + \frac{Z^{\frac{7}{2}} r^{2} (- \frac{\sqrt{6} {cos}^{2} θ}{512 \sqrt{π} ⅇ^{2 ⅈ φ} ⅇ^{\frac{Z r}{4 a}}} + \frac{\sqrt{6}}{512 \sqrt{π} ⅇ^{2 ⅈ φ} ⅇ^{\frac{Z r}{4 a}}})}{a^{\frac{7}{2}}}$
ψ_4,2,-1=	$- \frac{\sqrt{6} Z^{\frac{9}{2}} r^{3} sin θ cos θ}{3072 \sqrt{π} a^{\frac{9}{2}} ⅇ^{ⅈ φ} ⅇ^{\frac{Z r}{4 a}}} + \frac{\sqrt{6} Z^{\frac{7}{2}} r^{2} sin θ cos θ}{256 \sqrt{π} a^{\frac{7}{2}} ⅇ^{ⅈ φ} ⅇ^{\frac{Z r}{4 a}}}$
ψ_4,2,0=	$\frac{Z^{\frac{9}{2}} r^{3} (- \frac{{cos}^{2} θ}{1024 \sqrt{π} ⅇ^{\frac{Z r}{4 a}}} + \frac{1}{3072 \sqrt{π} ⅇ^{\frac{Z r}{4 a}}})}{a^{\frac{9}{2}}} + \frac{Z^{\frac{7}{2}} r^{2} (\frac{3 {cos}^{2} θ}{256 \sqrt{π} ⅇ^{\frac{Z r}{4 a}}} - \frac{1}{256 \sqrt{π} ⅇ^{\frac{Z r}{4 a}}})}{a^{\frac{7}{2}}}$
ψ_4,2,1=	$\frac{\sqrt{6} Z^{\frac{9}{2}} r^{3} ⅇ^{ⅈ φ} sin θ cos θ}{3072 \sqrt{π} a^{\frac{9}{2}} ⅇ^{\frac{Z r}{4 a}}} - \frac{\sqrt{6} Z^{\frac{7}{2}} r^{2} ⅇ^{ⅈ φ} sin θ cos θ}{256 \sqrt{π} a^{\frac{7}{2}} ⅇ^{\frac{Z r}{4 a}}}$
ψ_4,2,2=	$\frac{Z^{\frac{9}{2}} r^{3} (\frac{\sqrt{6} ⅇ^{2 ⅈ φ} {cos}^{2} θ}{6144 \sqrt{π} ⅇ^{\frac{Z r}{4 a}}} - \frac{\sqrt{6} ⅇ^{2 ⅈ φ}}{6144 \sqrt{π} ⅇ^{\frac{Z r}{4 a}}})}{a^{\frac{9}{2}}} + \frac{Z^{\frac{7}{2}} r^{2} (- \frac{\sqrt{6} ⅇ^{2 ⅈ φ} {cos}^{2} θ}{512 \sqrt{π} ⅇ^{\frac{Z r}{4 a}}} + \frac{\sqrt{6} ⅇ^{2 ⅈ φ}}{512 \sqrt{π} ⅇ^{\frac{Z r}{4 a}}})}{a^{\frac{7}{2}}}$
ψ_4,3,-3=	$\frac{Z^{\frac{9}{2}} r^{3} (- \frac{\sqrt{- {cos}^{2} θ + 1} {cos}^{2} θ}{6144 \sqrt{π} ⅇ^{3 ⅈ φ} ⅇ^{\frac{Z r}{4 a}}} + \frac{\sqrt{- {cos}^{2} θ + 1}}{6144 \sqrt{π} ⅇ^{3 ⅈ φ} ⅇ^{\frac{Z r}{4 a}}})}{a^{\frac{9}{2}}}$
ψ_4,3,-2=	$\frac{Z^{\frac{9}{2}} r^{3} (- \frac{\sqrt{6} {cos}^{3} θ}{6144 \sqrt{π} ⅇ^{2 ⅈ φ} ⅇ^{\frac{Z r}{4 a}}} + \frac{\sqrt{6} cos θ}{6144 \sqrt{π} ⅇ^{2 ⅈ φ} ⅇ^{\frac{Z r}{4 a}}})}{a^{\frac{9}{2}}}$
ψ_4,3,-1=	$\frac{Z^{\frac{9}{2}} r^{3} (\frac{\sqrt{15} sin θ {cos}^{2} θ}{6144 \sqrt{π} ⅇ^{ⅈ φ} ⅇ^{\frac{Z r}{4 a}}} - \frac{\sqrt{15} sin θ}{30720 \sqrt{π} ⅇ^{ⅈ φ} ⅇ^{\frac{Z r}{4 a}}})}{a^{\frac{9}{2}}}$
ψ_4,3,0=	$\frac{Z^{\frac{9}{2}} r^{3} (\frac{\sqrt{5} {cos}^{3} θ}{3072 \sqrt{π} ⅇ^{\frac{Z r}{4 a}}} - \frac{\sqrt{5} cos θ}{5120 \sqrt{π} ⅇ^{\frac{Z r}{4 a}}})}{a^{\frac{9}{2}}}$
ψ_4,3,1=	$\frac{Z^{\frac{9}{2}} r^{3} (- \frac{\sqrt{15} ⅇ^{ⅈ φ} sin θ {cos}^{2} θ}{6144 \sqrt{π} ⅇ^{\frac{Z r}{4 a}}} + \frac{\sqrt{15} ⅇ^{ⅈ φ} sin θ}{30720 \sqrt{π} ⅇ^{\frac{Z r}{4 a}}})}{a^{\frac{9}{2}}}$
ψ_4,3,2=	$\frac{Z^{\frac{9}{2}} r^{3} (- \frac{\sqrt{6} ⅇ^{2 ⅈ φ} {cos}^{3} θ}{6144 \sqrt{π} ⅇ^{\frac{Z r}{4 a}}} + \frac{\sqrt{6} ⅇ^{2 ⅈ φ} cos θ}{6144 \sqrt{π} ⅇ^{\frac{Z r}{4 a}}})}{a^{\frac{9}{2}}}$
ψ_4,3,3=	$\frac{Z^{\frac{9}{2}} r^{3} (\frac{\sqrt{- {cos}^{2} θ + 1} ⅇ^{3 ⅈ φ} {cos}^{2} θ}{6144 \sqrt{π} ⅇ^{\frac{Z r}{4 a}}} - \frac{\sqrt{- {cos}^{2} θ + 1} ⅇ^{3 ⅈ φ}}{6144 \sqrt{π} ⅇ^{\frac{Z r}{4 a}}})}{a^{\frac{9}{2}}}$
ψ_5,0,0=	$\frac{2 \sqrt{5} Z^{\frac{11}{2}} r^{4}}{234375 \sqrt{π} a^{\frac{11}{2}} ⅇ^{\frac{Z r}{5 a}}} - \frac{4 \sqrt{5} Z^{\frac{9}{2}} r^{3}}{9375 \sqrt{π} a^{\frac{9}{2}} ⅇ^{\frac{Z r}{5 a}}} + \frac{4 \sqrt{5} Z^{\frac{7}{2}} r^{2}}{625 \sqrt{π} a^{\frac{7}{2}} ⅇ^{\frac{Z r}{5 a}}} - \frac{4 \sqrt{5} Z^{\frac{5}{2}} r}{125 \sqrt{π} a^{\frac{5}{2}} ⅇ^{\frac{Z r}{5 a}}} + \frac{\sqrt{5} Z^{\frac{3}{2}}}{25 \sqrt{π} a^{\frac{3}{2}} ⅇ^{\frac{Z r}{5 a}}}$
ψ_5,1,-1=	$- \frac{2 \sqrt{5} Z^{\frac{11}{2}} r^{4} sin θ}{234375 \sqrt{π} a^{\frac{11}{2}} ⅇ^{ⅈ φ} ⅇ^{\frac{Z r}{5 a}}} + \frac{6 \sqrt{5} Z^{\frac{9}{2}} r^{3} sin θ}{15625 \sqrt{π} a^{\frac{9}{2}} ⅇ^{ⅈ φ} ⅇ^{\frac{Z r}{5 a}}} - \frac{3 \sqrt{5} Z^{\frac{7}{2}} r^{2} sin θ}{625 \sqrt{π} a^{\frac{7}{2}} ⅇ^{ⅈ φ} ⅇ^{\frac{Z r}{5 a}}} + \frac{2 \sqrt{5} Z^{\frac{5}{2}} r sin θ}{125 \sqrt{π} a^{\frac{5}{2}} ⅇ^{ⅈ φ} ⅇ^{\frac{Z r}{5 a}}}$
ψ_5,1,0=	$- \frac{2 \sqrt{10} Z^{\frac{11}{2}} r^{4} cos θ}{234375 \sqrt{π} a^{\frac{11}{2}} ⅇ^{\frac{Z r}{5 a}}} + \frac{6 \sqrt{10} Z^{\frac{9}{2}} r^{3} cos θ}{15625 \sqrt{π} a^{\frac{9}{2}} ⅇ^{\frac{Z r}{5 a}}} - \frac{3 \sqrt{10} Z^{\frac{7}{2}} r^{2} cos θ}{625 \sqrt{π} a^{\frac{7}{2}} ⅇ^{\frac{Z r}{5 a}}} + \frac{2 \sqrt{10} Z^{\frac{5}{2}} r cos θ}{125 \sqrt{π} a^{\frac{5}{2}} ⅇ^{\frac{Z r}{5 a}}}$
ψ_5,1,1=	$\frac{2 \sqrt{5} Z^{\frac{11}{2}} r^{4} ⅇ^{ⅈ φ} sin θ}{234375 \sqrt{π} a^{\frac{11}{2}} ⅇ^{\frac{Z r}{5 a}}} - \frac{6 \sqrt{5} Z^{\frac{9}{2}} r^{3} ⅇ^{ⅈ φ} sin θ}{15625 \sqrt{π} a^{\frac{9}{2}} ⅇ^{\frac{Z r}{5 a}}} + \frac{3 \sqrt{5} Z^{\frac{7}{2}} r^{2} ⅇ^{ⅈ φ} sin θ}{625 \sqrt{π} a^{\frac{7}{2}} ⅇ^{\frac{Z r}{5 a}}} - \frac{2 \sqrt{5} Z^{\frac{5}{2}} r ⅇ^{ⅈ φ} sin θ}{125 \sqrt{π} a^{\frac{5}{2}} ⅇ^{\frac{Z r}{5 a}}}$
ψ_5,2,-2=	$\frac{Z^{\frac{11}{2}} r^{4} (- \frac{\sqrt{21} {cos}^{2} θ}{328125 \sqrt{π} ⅇ^{2 ⅈ φ} ⅇ^{\frac{Z r}{5 a}}} + \frac{\sqrt{21}}{328125 \sqrt{π} ⅇ^{2 ⅈ φ} ⅇ^{\frac{Z r}{5 a}}})}{a^{\frac{11}{2}}} + \frac{Z^{\frac{9}{2}} r^{3} (\frac{\sqrt{21} {cos}^{2} θ}{9375 \sqrt{π} ⅇ^{2 ⅈ φ} ⅇ^{\frac{Z r}{5 a}}} - \frac{\sqrt{21}}{9375 \sqrt{π} ⅇ^{2 ⅈ φ} ⅇ^{\frac{Z r}{5 a}}})}{a^{\frac{9}{2}}} + \frac{Z^{\frac{7}{2}} r^{2} (- \frac{\sqrt{21} {cos}^{2} θ}{1250 \sqrt{π} ⅇ^{2 ⅈ φ} ⅇ^{\frac{Z r}{5 a}}} + \frac{\sqrt{21}}{1250 \sqrt{π} ⅇ^{2 ⅈ φ} ⅇ^{\frac{Z r}{5 a}}})}{a^{\frac{7}{2}}}$
ψ_5,2,-1=	$\frac{2 \sqrt{21} Z^{\frac{11}{2}} r^{4} sin θ cos θ}{328125 \sqrt{π} a^{\frac{11}{2}} ⅇ^{ⅈ φ} ⅇ^{\frac{Z r}{5 a}}} - \frac{2 \sqrt{21} Z^{\frac{9}{2}} r^{3} sin θ cos θ}{9375 \sqrt{π} a^{\frac{9}{2}} ⅇ^{ⅈ φ} ⅇ^{\frac{Z r}{5 a}}} + \frac{\sqrt{21} Z^{\frac{7}{2}} r^{2} sin θ cos θ}{625 \sqrt{π} a^{\frac{7}{2}} ⅇ^{ⅈ φ} ⅇ^{\frac{Z r}{5 a}}}$
ψ_5,2,0=	$\frac{Z^{\frac{11}{2}} r^{4} (\frac{\sqrt{14} {cos}^{2} θ}{109375 \sqrt{π} ⅇ^{\frac{Z r}{5 a}}} - \frac{\sqrt{14}}{328125 \sqrt{π} ⅇ^{\frac{Z r}{5 a}}})}{a^{\frac{11}{2}}} + \frac{Z^{\frac{9}{2}} r^{3} (- \frac{\sqrt{14} {cos}^{2} θ}{3125 \sqrt{π} ⅇ^{\frac{Z r}{5 a}}} + \frac{\sqrt{14}}{9375 \sqrt{π} ⅇ^{\frac{Z r}{5 a}}})}{a^{\frac{9}{2}}} + \frac{Z^{\frac{7}{2}} r^{2} (\frac{3 \sqrt{14} {cos}^{2} θ}{1250 \sqrt{π} ⅇ^{\frac{Z r}{5 a}}} - \frac{\sqrt{14}}{1250 \sqrt{π} ⅇ^{\frac{Z r}{5 a}}})}{a^{\frac{7}{2}}}$
ψ_5,2,1=	$- \frac{2 \sqrt{21} Z^{\frac{11}{2}} r^{4} ⅇ^{ⅈ φ} sin θ cos θ}{328125 \sqrt{π} a^{\frac{11}{2}} ⅇ^{\frac{Z r}{5 a}}} + \frac{2 \sqrt{21} Z^{\frac{9}{2}} r^{3} ⅇ^{ⅈ φ} sin θ cos θ}{9375 \sqrt{π} a^{\frac{9}{2}} ⅇ^{\frac{Z r}{5 a}}} - \frac{\sqrt{21} Z^{\frac{7}{2}} r^{2} ⅇ^{ⅈ φ} sin θ cos θ}{625 \sqrt{π} a^{\frac{7}{2}} ⅇ^{\frac{Z r}{5 a}}}$
ψ_5,2,2=	$\frac{Z^{\frac{11}{2}} r^{4} (- \frac{\sqrt{21} ⅇ^{2 ⅈ φ} {cos}^{2} θ}{328125 \sqrt{π} ⅇ^{\frac{Z r}{5 a}}} + \frac{\sqrt{21} ⅇ^{2 ⅈ φ}}{328125 \sqrt{π} ⅇ^{\frac{Z r}{5 a}}})}{a^{\frac{11}{2}}} + \frac{Z^{\frac{9}{2}} r^{3} (\frac{\sqrt{21} ⅇ^{2 ⅈ φ} {cos}^{2} θ}{9375 \sqrt{π} ⅇ^{\frac{Z r}{5 a}}} - \frac{\sqrt{21} ⅇ^{2 ⅈ φ}}{9375 \sqrt{π} ⅇ^{\frac{Z r}{5 a}}})}{a^{\frac{9}{2}}} + \frac{Z^{\frac{7}{2}} r^{2} (- \frac{\sqrt{21} ⅇ^{2 ⅈ φ} {cos}^{2} θ}{1250 \sqrt{π} ⅇ^{\frac{Z r}{5 a}}} + \frac{\sqrt{21} ⅇ^{2 ⅈ φ}}{1250 \sqrt{π} ⅇ^{\frac{Z r}{5 a}}})}{a^{\frac{7}{2}}}$
ψ_5,3,-3=	$\frac{Z^{\frac{11}{2}} r^{4} (\frac{\sqrt{- 2 {cos}^{2} θ + 2} {cos}^{2} θ}{187500 \sqrt{π} ⅇ^{3 ⅈ φ} ⅇ^{\frac{Z r}{5 a}}} - \frac{\sqrt{- 2 {cos}^{2} θ + 2}}{187500 \sqrt{π} ⅇ^{3 ⅈ φ} ⅇ^{\frac{Z r}{5 a}}})}{a^{\frac{11}{2}}} + \frac{Z^{\frac{9}{2}} r^{3} (- \frac{\sqrt{- 2 {cos}^{2} θ + 2} {cos}^{2} θ}{9375 \sqrt{π} ⅇ^{3 ⅈ φ} ⅇ^{\frac{Z r}{5 a}}} + \frac{\sqrt{- 2 {cos}^{2} θ + 2}}{9375 \sqrt{π} ⅇ^{3 ⅈ φ} ⅇ^{\frac{Z r}{5 a}}})}{a^{\frac{9}{2}}}$
ψ_5,3,-2=	$\frac{Z^{\frac{11}{2}} r^{4} (\frac{\sqrt{3} {cos}^{3} θ}{93750 \sqrt{π} ⅇ^{2 ⅈ φ} ⅇ^{\frac{Z r}{5 a}}} - \frac{\sqrt{3} cos θ}{93750 \sqrt{π} ⅇ^{2 ⅈ φ} ⅇ^{\frac{Z r}{5 a}}})}{a^{\frac{11}{2}}} + \frac{Z^{\frac{9}{2}} r^{3} (- \frac{2 \sqrt{3} {cos}^{3} θ}{9375 \sqrt{π} ⅇ^{2 ⅈ φ} ⅇ^{\frac{Z r}{5 a}}} + \frac{2 \sqrt{3} cos θ}{9375 \sqrt{π} ⅇ^{2 ⅈ φ} ⅇ^{\frac{Z r}{5 a}}})}{a^{\frac{9}{2}}}$
ψ_5,3,-1=	$\frac{Z^{\frac{11}{2}} r^{4} (- \frac{\sqrt{30} sin θ {cos}^{2} θ}{187500 \sqrt{π} ⅇ^{ⅈ φ} ⅇ^{\frac{Z r}{5 a}}} + \frac{\sqrt{30} sin θ}{937500 \sqrt{π} ⅇ^{ⅈ φ} ⅇ^{\frac{Z r}{5 a}}})}{a^{\frac{11}{2}}} + \frac{Z^{\frac{9}{2}} r^{3} (\frac{\sqrt{30} sin θ {cos}^{2} θ}{9375 \sqrt{π} ⅇ^{ⅈ φ} ⅇ^{\frac{Z r}{5 a}}} - \frac{\sqrt{30} sin θ}{46875 \sqrt{π} ⅇ^{ⅈ φ} ⅇ^{\frac{Z r}{5 a}}})}{a^{\frac{9}{2}}}$
ψ_5,3,0=	$\frac{Z^{\frac{11}{2}} r^{4} (- \frac{\sqrt{10} {cos}^{3} θ}{93750 \sqrt{π} ⅇ^{\frac{Z r}{5 a}}} + \frac{\sqrt{10} cos θ}{156250 \sqrt{π} ⅇ^{\frac{Z r}{5 a}}})}{a^{\frac{11}{2}}} + \frac{Z^{\frac{9}{2}} r^{3} (\frac{2 \sqrt{10} {cos}^{3} θ}{9375 \sqrt{π} ⅇ^{\frac{Z r}{5 a}}} - \frac{2 \sqrt{10} cos θ}{15625 \sqrt{π} ⅇ^{\frac{Z r}{5 a}}})}{a^{\frac{9}{2}}}$
ψ_5,3,1=	$\frac{Z^{\frac{11}{2}} r^{4} (\frac{\sqrt{30} ⅇ^{ⅈ φ} sin θ {cos}^{2} θ}{187500 \sqrt{π} ⅇ^{\frac{Z r}{5 a}}} - \frac{\sqrt{30} ⅇ^{ⅈ φ} sin θ}{937500 \sqrt{π} ⅇ^{\frac{Z r}{5 a}}})}{a^{\frac{11}{2}}} + \frac{Z^{\frac{9}{2}} r^{3} (- \frac{\sqrt{30} ⅇ^{ⅈ φ} sin θ {cos}^{2} θ}{9375 \sqrt{π} ⅇ^{\frac{Z r}{5 a}}} + \frac{\sqrt{30} ⅇ^{ⅈ φ} sin θ}{46875 \sqrt{π} ⅇ^{\frac{Z r}{5 a}}})}{a^{\frac{9}{2}}}$
ψ_5,3,2=	$\frac{Z^{\frac{11}{2}} r^{4} (\frac{\sqrt{3} ⅇ^{2 ⅈ φ} {cos}^{3} θ}{93750 \sqrt{π} ⅇ^{\frac{Z r}{5 a}}} - \frac{\sqrt{3} ⅇ^{2 ⅈ φ} cos θ}{93750 \sqrt{π} ⅇ^{\frac{Z r}{5 a}}})}{a^{\frac{11}{2}}} + \frac{Z^{\frac{9}{2}} r^{3} (- \frac{2 \sqrt{3} ⅇ^{2 ⅈ φ} {cos}^{3} θ}{9375 \sqrt{π} ⅇ^{\frac{Z r}{5 a}}} + \frac{2 \sqrt{3} ⅇ^{2 ⅈ φ} cos θ}{9375 \sqrt{π} ⅇ^{\frac{Z r}{5 a}}})}{a^{\frac{9}{2}}}$
ψ_5,3,3=	$\frac{Z^{\frac{11}{2}} r^{4} (- \frac{\sqrt{- 2 {cos}^{2} θ + 2} ⅇ^{3 ⅈ φ} {cos}^{2} θ}{187500 \sqrt{π} ⅇ^{\frac{Z r}{5 a}}} + \frac{\sqrt{- 2 {cos}^{2} θ + 2} ⅇ^{3 ⅈ φ}}{187500 \sqrt{π} ⅇ^{\frac{Z r}{5 a}}})}{a^{\frac{11}{2}}} + \frac{Z^{\frac{9}{2}} r^{3} (\frac{\sqrt{- 2 {cos}^{2} θ + 2} ⅇ^{3 ⅈ φ} {cos}^{2} θ}{9375 \sqrt{π} ⅇ^{\frac{Z r}{5 a}}} - \frac{\sqrt{- 2 {cos}^{2} θ + 2} ⅇ^{3 ⅈ φ}}{9375 \sqrt{π} ⅇ^{\frac{Z r}{5 a}}})}{a^{\frac{9}{2}}}$
ψ_5,4,-4=	$\frac{Z^{\frac{11}{2}} r^{4} (\frac{{cos}^{4} θ}{375000 \sqrt{π} ⅇ^{4 ⅈ φ} ⅇ^{\frac{Z r}{5 a}}} - \frac{{cos}^{2} θ}{187500 \sqrt{π} ⅇ^{4 ⅈ φ} ⅇ^{\frac{Z r}{5 a}}} + \frac{1}{375000 \sqrt{π} ⅇ^{4 ⅈ φ} ⅇ^{\frac{Z r}{5 a}}})}{a^{\frac{11}{2}}}$
ψ_5,4,-3=	$\frac{Z^{\frac{11}{2}} r^{4} (- \frac{\sqrt{- 2 {cos}^{2} θ + 2} {cos}^{3} θ}{187500 \sqrt{π} ⅇ^{3 ⅈ φ} ⅇ^{\frac{Z r}{5 a}}} + \frac{\sqrt{- 2 {cos}^{2} θ + 2} cos θ}{187500 \sqrt{π} ⅇ^{3 ⅈ φ} ⅇ^{\frac{Z r}{5 a}}})}{a^{\frac{11}{2}}}$
ψ_5,4,-2=	$\frac{Z^{\frac{11}{2}} r^{4} (- \frac{\sqrt{7} {cos}^{4} θ}{187500 \sqrt{π} ⅇ^{2 ⅈ φ} ⅇ^{\frac{Z r}{5 a}}} + \frac{2 \sqrt{7} {cos}^{2} θ}{328125 \sqrt{π} ⅇ^{2 ⅈ φ} ⅇ^{\frac{Z r}{5 a}}} - \frac{\sqrt{7}}{1312500 \sqrt{π} ⅇ^{2 ⅈ φ} ⅇ^{\frac{Z r}{5 a}}})}{a^{\frac{11}{2}}}$
ψ_5,4,-1=	$\frac{Z^{\frac{11}{2}} r^{4} (\frac{\sqrt{14} sin θ {cos}^{3} θ}{187500 \sqrt{π} ⅇ^{ⅈ φ} ⅇ^{\frac{Z r}{5 a}}} - \frac{\sqrt{14} sin θ cos θ}{437500 \sqrt{π} ⅇ^{ⅈ φ} ⅇ^{\frac{Z r}{5 a}}})}{a^{\frac{11}{2}}}$
ψ_5,4,0=	$\frac{Z^{\frac{11}{2}} r^{4} (\frac{\sqrt{70} {cos}^{4} θ}{375000 \sqrt{π} ⅇ^{\frac{Z r}{5 a}}} - \frac{\sqrt{70} {cos}^{2} θ}{437500 \sqrt{π} ⅇ^{\frac{Z r}{5 a}}} + \frac{\sqrt{70}}{4375000 \sqrt{π} ⅇ^{\frac{Z r}{5 a}}})}{a^{\frac{11}{2}}}$
ψ_5,4,1=	$\frac{Z^{\frac{11}{2}} r^{4} (- \frac{\sqrt{14} ⅇ^{ⅈ φ} sin θ {cos}^{3} θ}{187500 \sqrt{π} ⅇ^{\frac{Z r}{5 a}}} + \frac{\sqrt{14} ⅇ^{ⅈ φ} sin θ cos θ}{437500 \sqrt{π} ⅇ^{\frac{Z r}{5 a}}})}{a^{\frac{11}{2}}}$
ψ_5,4,2=	$\frac{Z^{\frac{11}{2}} r^{4} (- \frac{\sqrt{7} ⅇ^{2 ⅈ φ} {cos}^{4} θ}{187500 \sqrt{π} ⅇ^{\frac{Z r}{5 a}}} + \frac{2 \sqrt{7} ⅇ^{2 ⅈ φ} {cos}^{2} θ}{328125 \sqrt{π} ⅇ^{\frac{Z r}{5 a}}} - \frac{\sqrt{7} ⅇ^{2 ⅈ φ}}{1312500 \sqrt{π} ⅇ^{\frac{Z r}{5 a}}})}{a^{\frac{11}{2}}}$
ψ_5,4,3=	$\frac{Z^{\frac{11}{2}} r^{4} (\frac{\sqrt{- 2 {cos}^{2} θ + 2} ⅇ^{3 ⅈ φ} {cos}^{3} θ}{187500 \sqrt{π} ⅇ^{\frac{Z r}{5 a}}} - \frac{\sqrt{- 2 {cos}^{2} θ + 2} ⅇ^{3 ⅈ φ} cos θ}{187500 \sqrt{π} ⅇ^{\frac{Z r}{5 a}}})}{a^{\frac{11}{2}}}$
ψ_5,4,4=	$\frac{Z^{\frac{11}{2}} r^{4} (\frac{ⅇ^{4 ⅈ φ} {cos}^{4} θ}{375000 \sqrt{π} ⅇ^{\frac{Z r}{5 a}}} - \frac{ⅇ^{4 ⅈ φ} {cos}^{2} θ}{187500 \sqrt{π} ⅇ^{\frac{Z r}{5 a}}} + \frac{ⅇ^{4 ⅈ φ}}{375000 \sqrt{π} ⅇ^{\frac{Z r}{5 a}}})}{a^{\frac{11}{2}}}$

Due to memory limitations you have to request wave functions for 5<n≤20 one by one via the default form.

hydrogen-wavefunction.info

Table of normalised hydrogen wavefunctions |Ψn,l,m⟩

Table of normalised hydrogen wavefunctions |Ψ_n,l,m⟩