1. The problem statement, all variables and given/known data Since Hamiltonian operator is: Ĥ = - (ħ2/(2m))(delta)2 - A/r where r = (x2+y2+z2) (delta)2 = ∂2/∂x2 + ∂2/∂y2 + ∂2/∂z2 A = a constant from Ĥg(r) = Eg(r) form, where: g(r) = D e-r/b(1-r/b) with b, D as constants, is an EIGENFUNCTION of Ĥ, find the correct b and give the eigenvalue E. 2. Relevant equations g(r) = D e-r/b(1-r/b) Ĥ = - (ħ2/(2m))(delta)2 - A/r where r = (x2+y2+z2) (delta)2 = ∂2/∂x2 + ∂2/∂y2 + ∂2/∂z2 D = a constant 3. The attempt at a solution g(r) = D e-r/b(1-r/b) g'(r) = -De-r/b/b - De-r/b/b + Dre-r/b/b2 = -2De-r/b/b + Dre-r/b/b2 g''(r) = 3De-r/b/b2 - Dre-r/b/b3 [delta_g(r)]2 = 5De-r/b/b2 -Dre-r/b/b3 - 4De-r/b/(br) Ĥg(r) = Eg(r) - (ħ2/(2m))(5De-r/b/b2 -Dre-r/b/b3 - 4De-r/b/(br)) - A/r * (D e-r/b(1-r/b)) = E*D e-r/b (1-r/b) ..which is then reduced to: -5ħ2/(2mb2) + ħ2r/(2mb3) + 4ħ2/(2mbr) - A/r + A/b = E (1-r/b)....I managed to cancel out constant D and e-r/b, but I am at loss how how to eliminate r? Should I equivelate: ħ2r/(2mb3) + 4ħ2/(2mbr) - A/r = -E(r/b) ? I tried this way, and still haven't managed to find a way to cancel out r....to make b an independent number... With regard to E, if I am not wrong, I think Energy is that of an excited state, NOT ground state, except I haven't figured it out (for I have not gotten b constant), and have no idea which energy level it is.... Any hints or notices to my mistakes would be appreciated!