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Circular Coulomb bound state

For $R(r)\propto r^l e^{-r/[a(l+1)]}$, the radial probability density is proportional to $r^{2l+2}e^{-2r/[a(l+1)]}$ and
$$
\langle r\rangle=\frac{(2l+3)(l+1)}2a.
$$


Mean radius of a circular Coulomb bound state

Past exam of the mathematics course of the University of Cambridge / 2018 / ib / Paper 2 / 17B / Solution

Past exam of the mathematics course of the University of Cambridge / 2024 / ib / Paper 1 / 14A / iii / Solution

Mean radius of a circular Coulomb bound state

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Mean radius of a circular Coulomb bound state

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