# Ground state energy $E_{0}$ and evaluation of physical energies

Given the lowest eigenvalue $E_0$ of an Schrödinguer operator, do the other energies $E_{n}$ for $n >0$ depend strongly on the lowest eigenvalue of the system? I mean, if we somehow fixed the eigenvalue $E_{0}$, could we get more or at least better approximations to the other eigenenergies of the system?

thanks

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No. The differences between the eigenvalues (giving the spectral frequencies) are highly specific for each chemical substance, so knowledge of $E_0$ tells very little about the remainder of the spectrum.