2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/97091We investigate the bound states of the Yukawa potential $V(r)=-λ\exp(-αr)/ r$, using different algorithms: solving the Schrödinger equation numerically and our Monte Carlo Hamiltonian approach. There is a critical $α=α_C$, above which no bound state exists. We study the relation between $α_C$ and $λ$ for various angular momentum quantum number $l$, and find in atomic units, $α_{C}(l)= λ[A_{1} \exp(-l/ B_{1})+ A_{2} \exp(-l/ B_{2})]$, with $A_1=1.020(18)$, $B_1=0.443(14)$, $A_2=0.170(17)$, and $B_2=2.490(180)$.15 pages, 12 figures, 5 tables. Version to appear in Sciences in China GHigh Energy Physics - PhenomenologyQuantum Physicstext