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Homework Help: Can someone check this please

  1. Mar 9, 2010 #1
    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.
     
  2. jcsd
  3. Mar 10, 2010 #2
    You might need to show us your work, but imaginary normalization constants are perfectly reasonable. Since the only measurable quantity is:

    [tex]\psi^{\dagger} \psi[/tex]

    Which shouldn't have any imaginary component in it.

    Also, I think you mean to say:

    [tex]z = r cos(\theta)[/tex]
     
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