The radial distribution function (RDF) is defined variably in literature, either as 4πr²R(r)² or r²R(r)². The inclusion of the 4π factor is essential when calculating volume, while the simpler form is used for area calculations, particularly in determining particle radial probability. This distinction arises from the normalization of the wavefunction, represented by the integral ##\int_{\mathbb{R}^3}drd\theta d\varphi \left| \Psi(r,\theta,\varphi) \right|^2 = 1##. Understanding these definitions is crucial for accurate computations in quantum mechanics.
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