I have came across an interesting question in the book(adsbygoogle = window.adsbygoogle || []).push({}); Laser Physicsby Milonni, the question is as follows:

The binding energy of the ion H_{2}^{+}( the energy required to separate to infinity the two protons and the electron) is -16.3 eV at the equilibrium separation 0.106 nm.

(a) What is the contribution to the energy from the Coulomb repulsion of the nuclei?

(b) What is the contribution to the energy from the Coulomb attraction of the electron to the nuclei?

(c) The Hellman-Feynman theorem says, in effect, that the force between the nuclei in a molecule can be calculated from the electrostatic repulsion between the nuclei and the electrostatic attraction of the nuclei to the electron distribution. According to this theorem, where must the squared modulus of the electron wave function in H_{2}^{+}have its maximum value?

(d) Estimate the rotational constant B_{e}for H_{2}^{+}, and compare your result with the value 29.8 cm^{-1}tabulated in Herzberg's Spectra of Diatomic Molecules.

I have found in the part (a)to be +13.58 eV by the familiar formula for Coulomb potential and part (b) to be -29.88 eV. By subtracting the result of part (a) from the given binding energy. Firstly I would like to ask if these are correct and secondly I have no idea on how to proceed in part (c) as I have only taken an introductory course on quantum physics. Can you give me some hints? Any help is appreciated.

Thanks

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# Hellman-Feyman Theorem

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