How Do You Expand a Hydrogen Atom State in an Orthonormal Basis?

[carlosbgois]

Homework Statement

[/B]
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 {Φ_nlm} basis of normalized eigenfunctions

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

Homework Equations

The result should be

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

The Attempt at a Solution

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

 

[blue_leaf77]

You are required to show any of your initial effort before others can help you.

 

[Avodyne]

Do you understand the general principle of writing a state as a linear combination of orthonormal basis states? And how, in general, to determine the coefficients?