Solving Normalization Factor for 1s Atomic Orbital of H

[geronimo123]

Hi all! I hope somebody is able to help me on my way with this question.

I have been asked to show that the Normalization factor for the 1s atomic orbital of H is $$1/(\Pi a_o^3)^\frac{1}{2}$$. The wavefunction is $$\psi(r) = N exp(-r / a_o)$$

I'm given $$dt = r^2 sin \Theta$$ and $$dr d\Theta d\Phi$$ and $$\int_{0}^{\infty}x^n e^a^x dx=n!/a^n+1$$

I must admit I'm clueless which direction to go. It was mentioned to me, that squaring the wavefunction is the first step, but I cannot arrive at the given constant. Am I starting off on the wrong foot?

Thanks for any input, in advance.

geronimo

 

[nrqed]

Hi all! I hope somebody is able to help me on my way with this question.

I have been asked to show that the Normalization factor for the 1s atomic orbital of H is $$1/(\Pi a_o^3)^\frac{1}{2}$$. The wavefunction is $$\psi(r) = N exp(-r / a_o)$$

I'm given $$dt = r^2 sin \Theta$$ and $$dr d\Theta d\Phi$$ and $$\int_{0}^{\infty}x^n e^ax dx=n!/a^n+1$$

I must admit I'm clueless which direction to go. It was mentioned to me, that squaring the wavefunction is the first step, but I cannot arrive at the given constant. Am I starting off on the wrong foot?

Thanks for any input, in advance.

geronimo

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[geronimo123]

Sorry about this - I don't know how it managed to post twice. It's my first time working with tex and I was having evident difficulties :) Thanks for the pointer!