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Nuclear physics is the study of the composition, behavior and interaction of atomic nuclei and their constituent parts.
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How does the inter-atomic distance affect the energy of an electron?
The Hamiltonian of a your $H_2^+$ molecule is given by
$$\hat{H} = \hat{T}_\text{electron} + \hat{T}_\text{nuclei} + \hat{V}_\text{electron-nucleus} + \hat{V}_\text{nucleus-nucleus}.$$
If you want to …