In[1]:=

Psi[r_, z_, n_, l_, m_] = Exp[-Sqrt[(r^2 + z^2)]/2] * Sqrt[r^2 + z^2]^l * LaguerreL[n - l - 1, 2l + 1, Sqrt[r^2 + z^2]] * SphericalHarmonicY[l, m, ArcTan[r/z], 0]

Out[1]=

^(-1/2 (r^2 + z^2)^(1/2)) (r^2 + z^2)^(l/2) LaguerreL[-1 - l + n, 1 + 2 l, (r^2 + z^2)^(1/2)] SphericalHarmonicY[l, m, ArcTan[r/z], 0]

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