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Let $$ H = H_e + T_n $$ Where $H$ is the full Hamiltonian and $T_n$ is the nuclear kinetic energy. Notice that the only dependence on $R$ in $H_e$ is through the position operator, i.e. there is no dependence on $\frac{\partial}{\partial R}$. This means we can treat $H_e(R)$ as a (Hermitian) operator on the space of functions of $r$ for a fixed value of $R$. ...


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