My apologies, its not third order. The question gives the laplacian as :
$$ \nabla^2 = \frac{\mathrm{d^2} }{\mathrm{d} r^2} + \frac {2}{r} \frac{\mathrm{d} }{\mathrm{d} r} $$
Homework Statement
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The Hamiltonian and wavefunction for the ground state of the hydrogen atom H(1s1) are given,
in atomic units, as ## \hat {H} = - \frac{1}{2} \nabla^2 - \frac {1}{r} ## and ## \phi(1s) = \sqrt {\frac {1}{\pi }} e^{-r} ## . Using the radial portion of the Laplacian in the...