3 problems

Continuum-smearing conjecture. Because the discrete and continuous parts are proximate, and interactions beyond the random-phase approximation (RPA) are expected to smear discrete…

RPA correlation-energy conjecture. Even with attractive potentials, the RPA formula for the correlation energy applies as long as the logarithm in $E_N^{\operatorname{RPA}}$ does n…

Spectral convergence conjecture. The difference in convergence rates between the Lanczos approach applied to the Hermitian TDA Hamiltonian and to $H^{\text{no coupl}}$ is due to di…