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Hydrogen atom state expansion

  1. Sep 10, 2015 #1
    1. The problem statement, all variables and given/known data

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

    [tex]\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)[/tex]

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

    [tex]\phi_{nlm}(\mathbf{r})=R_{nl}(r)Y_l^m(\theta,\phi)[/tex]

    2. Relevant equations

    The result should be

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

    3. The attempt at a solution

    Apart from having the supposed solution, I have no idea where to start.
    Any help is appreciated.
     
  2. jcsd
  3. Sep 10, 2015 #2

    blue_leaf77

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    You are required to show any of your initial effort before others can help you.
     
  4. Sep 10, 2015 #3

    Avodyne

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    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?
     
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