Can someone check this please

1. The problem statement, all variables and given/known data

I am giving the following wave function which describes a hydrogen state:

[tex]\psi(r, 0) = (\frac{A}{\sqrt{\pi}})(\frac{1}{a_{0}})^{3/2} exp(-\frac{r}{a_{0}}) + (1/\sqrt{12*\pi})(\frac{z - \sqrt(2)x}{r})R_{21}[/tex]

Where [tex]R_{21}[/tex] is the radial equation.

I must rewrite [tex]\psi[/tex] in terms of summed eigenstates [tex]\psi_{nlm}[/tex].



2. Relevant equations

I assumed [tex]x = rsin\theta cos \varphi[/tex] and [tex]y = rcos\theta[/tex]



3. The attempt at a solution

I come up with four different eigenstates, but one of them has a (-1) coefficient (which leads to an imaginary normalization constant, A).

I don't see what I could have done wrong though.