Hydrogen Wave Function Homework Problem

AI Thread Summary
The discussion revolves around a homework problem involving the normalization of a hydrogen atom wave function expressed as a linear combination of eigenfunctions. The main challenge is to find the normalization constant A, given the state equation. Participants express confusion about the need to remember specific equations for the radial part R and the recursion formula for coefficients, as these were not provided in the exam. The normalization condition is emphasized, requiring the integral of the product of the wave function and its complex conjugate to equal one. Overall, the conversation highlights the complexities of memorizing necessary equations for solving quantum mechanics problems.
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Homework Statement


A problem from an examination:
A hydrogen atom is in the state
\Psi=A(\sqrt{6}\psi_{100}+\sqrt{2}\psi_{200}+\psi_{211}+2\psi_{31-1}+\sqrt{3}\psi_{321}+3\psi_{32-2})
where \psi_{nlm} are the eigenfunctions of hydrogen. Find A so that the equation is normalized.

Homework Equations


\psi_{nlm}=R_{nl}Y^m_l,\ \ \ Y^m_l=AP^m_l(cos\theta)

The Attempt at a Solution


Well I can get the angular parts for Y from some handbook. But in the test no additional data is provided, so should I just remember the equations for R to get the problem solved.

I mean... in another problem it was told:
"Remember that a_{+}\psi=\sqrt(n+1)\psi_{n+1}"

and then suddenly I have to remember how to get Rnl?
Well, ok.

I can remember that (according to Griffiths)
R_{nl}=\frac{1}{\rho}(\rho)^{l+1}\nu(\rho),\ \ \ \rho=\frac{r}{an}

But then I also have to remember the recursion formula for the coefficients of \nu(\rho)?

I can understand if that stuff is really something one needs to memorize, but what I find confusing is that in several cases stuff far easier to remember is given along with the problem. Which leads me to think I've gotten something wrong... that it shouldn't be this complex.
 
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offtop: totally agree with you about memorizing all this coeffs and formulas.

normalization condition is:
\int_{-\infty}^{\infty}\Psi \Psi^{*} = 1
where \Psi^{*} is http://en.wikipedia.org/wiki/Complex_conjugation" of \Psi

so, introduce your \Psi in integral, and get A from there.
 
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