Conversion of hydrogen atom wave function that I don't understand

AI Thread Summary
The discussion centers on the conversion of the hydrogen atom wave function, specifically the expression involving the normalization constant N and the variables r and θ. The participant seeks clarification on why z is represented as r cos θ rather than simply being the atomic number. Another user confirms that z indeed represents the z-component in spherical coordinates, clarifying the relationship between z, r, and θ. This exchange highlights the importance of understanding coordinate transformations in quantum mechanics. The conversation concludes with appreciation for the clarification provided.
adh2
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Hello!

I'm preparing for my quantum mechanics test. In the solutions of an old test I find this conversion, that I don't understand.

\Psi = Nze^{-r/2a_0} = Nre^{-r/2a_0}cos\Theta

N is the normalization constant, which is to be calculated. I would have guessed that z is the atomic number ( =1), but it is apparently = r cos \Theta. Can anyone please explain this to me?


Alfred
 
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Welcome to PF!

Hello Alfred! Welcome to PF! :wink:

I'm guessing :redface:, but it looks as if z is the component in the z-direction, and r and θ are the usual spherical coordinates, so that z = rcosθ. :smile:
 
Yes! That's it. Many thanks Tiny-Tim! :smile:
 
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