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

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SUMMARY

The discussion centers on the conversion of the hydrogen atom wave function in quantum mechanics, specifically the expression \(\Psi = Nze^{-r/2a_0} = Nre^{-r/2a_0}cos\Theta\). The variable \(z\) represents the z-component in spherical coordinates, defined as \(z = r \cos \Theta\), rather than the atomic number. The normalization constant \(N\) is also mentioned as a crucial element to be calculated for the wave function.

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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.

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

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 [tex]= r cos \Theta[/tex]. 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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