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I have thought about it but couldn't figure out how can I find the potential energy given the energy states, I mean for example in Lennard Jones potential there is a finite number of discrete quantum states so how could you find the potential if there is only a few number of states to fit a potential curve, does exist a rule to find it?

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    $\begingroup$ No solution in general. This is essentially the problem of hearing the shape of a drum. $\endgroup$ Oct 24, 2022 at 22:13

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If you know precisely all the energy eigenstates $|E_i\rangle$ of a Hamiltonian $H = K + V$ and know how to express the kinetic term $K$ in terms of it, then you know $V$ by decomposing $H$ and $K$ in the energy eingenbasis: $$V = \sum_{i,j} (E_i \delta_{ij}- \langle E_i|V|E_j\rangle) |E_i\rangle\langle E_j| $$

In the case of a potential well for which there is only a finite number of bound states, such as the Lennard-Jones', there are still an infinite number of scattering states that are energy eigenstates.

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