It is proved that the quantum mechanical Hamiltonian H = Σi=1N (p2 + m2) 1 2 - κ Σi>j|xi - xj|-1 for bosons (resp, fermions) is bounded from below if N ≤ cbκ-1 (resp. N ≤ cfκ -3 2). H is unbounded from below if N ≥ cblκ-1 (resp. N ≥ cflκ -3 2). The constants cb and cbl (resp. cf and cfl) differ by about a factor 2 (resp. 4).
All Science Journal Classification (ASJC) codes
- Physics and Astronomy(all)