For the hydrogen atom in its ground state, calculate (a) the probability density \( \psi^{2}(r) ...

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For the hydrogen atom in its ground state, calculate (a) the probability density \( \psi^{2}(r) \) and (b) the radial probability density \( P(r) \) for \( r=a \), where \( a \) is the Bohr radius.
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