- #1

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- Homework Statement
- Can the zero-point energy of diatomic hydrogen be calculated as a sum of the zero-point energies of all particles in the system?

- Relevant Equations
- ##E_1 = h^2/8mL^2##

If we take ##H_2## as a "particle" in a box, can the zero-point energy of the overall molecule be calculated as the sum of the zero-point energies of all particles in ##H_2##?

That is $$E_ {1,H_2}=\frac{2h^2}{8m_{\mathrm{H^+}}L^2} + \frac{2h^2}{8m_{\mathrm{e^-}}L^2}= \frac{h^2}{4L^2}(1/m_{\mathrm{H^+}}+1/m_{\mathrm{e^-}})$$

My reasoning being that in our "ideal" box, the system is isolated, and thus energy must be conserved.

That is $$E_ {1,H_2}=\frac{2h^2}{8m_{\mathrm{H^+}}L^2} + \frac{2h^2}{8m_{\mathrm{e^-}}L^2}= \frac{h^2}{4L^2}(1/m_{\mathrm{H^+}}+1/m_{\mathrm{e^-}})$$

My reasoning being that in our "ideal" box, the system is isolated, and thus energy must be conserved.