1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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]
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook