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I built a small program to show that the normalized hydrogen wave function (ground state) integrates to unity, as expected. But I got an absurd value: 4.6x10^19 instead.

I spanned a big volume (30 Bohr's radius) calculating and summing the product dr*dphi*dtheta * psi * psi.

Worse yet, when I choose a different discretization for the radial distance, I get very different value for the resulting probability.

Where am I missing the point?

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# Normalized wave function

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