Hydrogen atom state expansion

1. Sep 10, 2015

carlosbgois

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

Consider a hydrogen atom which, in t = 0, is in the state given by

$$\psi(\mathbf{r},t>0)=\frac{A}{4\pi}R_{10}(r)+\frac{cos\alpha}{4\pi}\left(\frac{z-\sqrt{2}x}{r}\right)R_{21}(r)$$

Expand ψ in terms of the nlm} basis of normalized eigenfunctions

$$\phi_{nlm}(\mathbf{r})=R_{nl}(r)Y_l^m(\theta,\phi)$$

2. Relevant equations

The result should be

$$A\phi_{100}(\mathbf{r})+\frac{cos\alpha}{\sqrt{3}}[\phi_{210}(\mathbf{r})+\phi_{211}(\mathbf{r})-\phi_{21,-1}(\mathbf{r})]$$

3. The attempt at a solution

Apart from having the supposed solution, I have no idea where to start.
Any help is appreciated.

2. Sep 10, 2015