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

Question

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

Answer 1

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.