I ran this in Mathematica 13.1:
u = Sqrt[1/10] (2*Exp[-r/a]/Sqrt[Pi a^3] + r Cos[x] Exp[-r/(2 a)]/(4 a Sqrt[2 Pi a^3]) - Sqrt[2] r Sin[x] Exp[-r/(2 a) + I y]/(8 a Sqrt[Pi a^3] ) + Sqrt[3] r Sin[x] Exp[-r/(2 a) - I y]/(8 a Sqrt[Pi a^3]))
Refine[FullSimplify[Conjugate[u]], Assumptions -> {r > 0, a > 0, x \[Element] Reals, y \[Element] Reals}]
But it could not give its conjugation:
How to solve this please?