Hydrogen atom wave functions

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

I solved the Schrödinger equation, obtaining a wave function in terms of Radial and the spherical harmonics as follows:

$$Ψ(r,0)= AR_{10} Y_{00} + \sqrt{\frac23} R_{21} Y_{10} + \sqrt{\frac23} R_{21} Y_{11} – \sqrt{\frac23} R_{21} Y_{1,-1}$$

2. Relevant equations

3. The attempt at a solution
The constant A is equal to i; is this result right or not?


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