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The subject is few-body quantum mechanics. Given a system of $N$ identical fermions (spin 1/2) interacting through pairwise potentials $V_{ij}$, how does the binding energy change between $N$ and $N+1$? Obviously this depends on the potential, so say it is the attractive Coulomb case:

$$V_{ij} = -\frac{1}{r_{ij}}$$

Both intuitive and analytical explanations are welcome.

Where I am at regarding this:

An estimate on the binding energy can be found using the variational principle, but this method gives only a lower bound on the binding energy. In general, this lower bound seems to decrease as $N$ increases (the system may be less bound). As the bound may be decreasing due to insufficiency in the variational wave function approximating the system, I cannot conclude that the binding energy is decreasing, let alone by how much.

Classically, I am thinking that, if a system of $N$ particles is bound, then adding another particle to the mix (increasing the total energy) increases the likelihood that one particle may gain energy enough to escape. I would expect this effect to diminish as $N$ increases. Although, the virial theorem states that $KE \approx -1/2 PE$, which may counteract this effect as $N$ increases. However, I am not sure how far any of this this extends to the quantum case.

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    $\begingroup$ What is the application? Identical fermions repel each other. $\endgroup$ – my2cts Feb 6 at 8:33
  • $\begingroup$ The application is in particle physics theory. Identical fermions would attract if interacting via a scalar mediator, I think, so I'm not sure if they have to repel each other. $\endgroup$ – alefs Feb 6 at 15:37
  • $\begingroup$ this is rather vague. Superconductivity, perhaps? $\endgroup$ – my2cts Feb 6 at 22:11

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