3 problems

Low-density Bose-gas conjecture. The formula above requires only a positive scattering length and the absence of any many-body, negative-energy bound state.

Let $z$ denote the model parameter, and let the symmetric and anti-symmetric ground state energies be approximated as in equation. The coefficients satisfy $w_1 \approx 0.6$,…

Continuity and piecewise-smoothness conjecture. For every finite $N$, the ground-state curve is continuous in $\alpha$ and piecewise smooth, and the number of its smooth pieces gro…