The wavefunction of hydrogen is given by(adsbygoogle = window.adsbygoogle || []).push({});

[tex]

\psi_{nlm}(r, \theta, \phi) = R_{nl}(r)Y_{lm}(\theta, \phi)

[/tex]

If I am only given the radial part, and asked to find the expectation value of the radial part I integrate the square of the wavefunction multiplied by r cubed allowing r to range from 0 to infinity. I don't understand where the extra factor of r squared comes from? I suspect it has something to do with multiplying by a volume element, but it is unclear to me why the factor of 4 pi that would normally come with spherical integration that depends on r alone disappears. I missed this on a test, recently, and was hoping someone could explain.

Thanks.

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# The expectation value for the radial part of the wavefunction of Hydrogen.

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