Finding a Complex Conjugate value of wave function

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First, sorry for my poor English and any impolite behavior might happen.

Here's two wave function(pic1) and problem below(pic2).
and they are polar coordinate problem ψ(r,θ,Φ)
You can see, problem requires conjugate function of ψ1.
Is it possible to find one? or is there a possibility that actually, problem requires complex conjugate function of ψ2? (I mean, error of problem)

I have withdrew from school temporarily. so there's no one whom I can ask about this.
so if you can't answer it directly, please tell me how I can find matters about this subject.

PS. There's no trouble integrating problem(pic2). It is actually from my textbook. but as I said, I'm studying it by myself, and I just want to know whether I can find a complex conjugate. So if you just confirm its possibility about complex conjugate value, I will appreciate you.

Regards and sorry for my poor English again. :)
 

fresh_42

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I assume ##a_0,r \in \mathbb{R}##, in which case the conjugate of ##\Psi_1## is ##\Psi_1## again. You get the conjugate of ##\Psi_2## by changing ##e^{i\theta}## to ##e^{-i\theta}\,.##
 

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