多重积分习题

The function
$\displaystyle \Psi(r)=A\left(2-\cfrac{Zr}a\right)e^{-Zr/2a}$
gives the form of the quantum-mechanical wavefunction representing the electron
in a hydrogen-like atom of atomic number $Z$, when the electron is in its first
allowed spherically symmetric excited state. Here $r$ is the usual spherical polar
coordinate, but, because of the spherical symmetry, the coordinates $\theta$ and $\phi$ do
not appear explicitly in $\Psi$. Determine the value that $A$ (assumed real) must have
if the wavefunction is to be correctly normalised, i.e. if the volume integral of
$|\Psi|^2$ over all space is to be equal to unity.
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