Effective potential determining one‐dimensional Slater sum in independent‐particle theory Available to Purchase

Hilton, March, and Curtis have earlier focused on the utility of the effective potential U(r,β) in determining the Slater sum Z(r,β)=Z₀(β)exp(−βU(r,β)). Here an explicit, though highly nonlinear, partial differential equation is derived for determining the effective potential U(x,β) in one‐dimensional problems. Direct solution of this equation by power series expansion in β leads readily to Husimi’s results obtained from off‐diagonal density matrix calculations. Perturbation theory in the potential is also developed, and thereby it is shown that an infinite subseries of the Husimi expansion is readily summed, and that a scaling property is exhibited.