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1.Question.

the unnormalized excited state wavefuction of the H atom is:

[tex]\psi = ( 2 - r/a_0 ) e^a[/tex]

where a = [tex]-r/a_0[/tex]

Normalize the function to one.

2. My attempts.

I tried 'integrating' the psi*psi, i.e. I squared the above wavefuction.

[tex]N^2\int_{0}^{\infty} R^2e^{2a}\int_{0}^{\pi}sin \theta d\theta\int_{0}^{2\pi}d\phi =1[/tex]

From here, I got confused with the examples. The second and third integrations were obviously 2 and [tex]2\pi[/tex], but the first integration I'm getting confused as to what to put as [tex]R^2[/tex] and I'm getting the same answer as the examples because when I done the calculation, the power to which R is the same with every question, which was [tex]a^3_0/4[/tex]

Hence: [tex]a^3_0/4*2*2\pi[/tex] =[tex] 1/N^2[/tex]

Hence I worked out N from this equation, but the answer I got was:

[tex]\psi =(1/\pi a^3_0)^{1/2}e^{-r/a_0}[/tex]

Which is the same as every other damn normalized wavefuction in the book.

I think I'm having trouble actually understanding how [tex]R^2[/tex] is translated from the original wavefuction to the actual integration, hence my immense trouble to working out what R is. Can anyone help with this?

the unnormalized excited state wavefuction of the H atom is:

[tex]\psi = ( 2 - r/a_0 ) e^a[/tex]

where a = [tex]-r/a_0[/tex]

Normalize the function to one.

2. My attempts.

I tried 'integrating' the psi*psi, i.e. I squared the above wavefuction.

[tex]N^2\int_{0}^{\infty} R^2e^{2a}\int_{0}^{\pi}sin \theta d\theta\int_{0}^{2\pi}d\phi =1[/tex]

From here, I got confused with the examples. The second and third integrations were obviously 2 and [tex]2\pi[/tex], but the first integration I'm getting confused as to what to put as [tex]R^2[/tex] and I'm getting the same answer as the examples because when I done the calculation, the power to which R is the same with every question, which was [tex]a^3_0/4[/tex]

Hence: [tex]a^3_0/4*2*2\pi[/tex] =[tex] 1/N^2[/tex]

Hence I worked out N from this equation, but the answer I got was:

[tex]\psi =(1/\pi a^3_0)^{1/2}e^{-r/a_0}[/tex]

Which is the same as every other damn normalized wavefuction in the book.

I think I'm having trouble actually understanding how [tex]R^2[/tex] is translated from the original wavefuction to the actual integration, hence my immense trouble to working out what R is. Can anyone help with this?

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