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

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?

Best regards,
Alfred

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tiny-tim
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Welcome to PF!

Hello Alfred! Welcome to PF!

I'm guessing , 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.

Yes! That's it. Many thanks Tiny-Tim!