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The central term in the hamiltonian formalism. Can be interpreted as an energy input, or "true" energy.

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Center of mass Hamiltonian of a Hydrogen atom

You are right; Hamiltonian for center of mass of hydrogen atom should be : $H=\displaystyle\frac{p^2}{2(m+m_e)}$ Where $p$ is momentum of Hydrogen atom (please check what is $p$ in your book). …
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