Definition Radial distribution function

[Pluto]

In some books the radial distribution function is defined as 4pi*r^2*R(r)^2 and in others as r^2*R(r)^2. Thus, a factor of 4pi is differing. Which expression is correct and why?

 

[soarce]

This factor may come from the normalization of the wavefunction $\int_{\mathbb{R}^3}drd\theta d\varphi \left| \Psi(r,\theta,\varphi) \right|^2 = 1$.

 

[julcab12]

If you want to compute for volume use 4pi; while the other is Area -- used in computing particle radial probability of Area and Volume. Link below.. http://hyperphysics.phy-astr.gsu.edu/hbase/quantum/hydwf.html#c3