Question

Hi can someone please help me understand how problem 1 is solved?

In the class lecture notes, the result of the first-order perturbation calculation for the energy of lithium was given as E-24.2 +1.-K... This energy is added to the Evalue obtained by treating each electron as if it were in an independent hydrogen-like orbital in order to estimate the total energy of the lithium atom. The calculation to determine the energy correction involves solving many integrals because the wavefunction for lithium has 6 terms, the Hamiltonian has 3 pairwise electron-electron potential terms and E"-("A"/"). Two of the many integrals are shown below. Show all of the work necessary to evaluate these integrals in terms of J, and Ky Sus (1)a'()'(2)8(2)28(2)110) * K-1)()+(2)8(2)21(3)a(3)dr 2. Sur (1)a (1)15+(2)$(2)28 (3)a (3) 2(1)(1)(2)B(2)15(3)a(3)dt

Im not sure what else i can add, besides that i understand that J(ij) refers to the Coulomb integral and that K(ij) refers to the exchange integral. if there is anything else to add please let me know.

Answer 1

If any queries please comment I will help you

can see for both integrees Ge - both integrals we so (3) & (3) so (1) a(1) SB (2) B (2) Of thorormality of spin states first integral || 42 de=da, de dag 3,1-flis"(1943(1)][is'12)4s(2] dt, dto '25°(1) 256) dez) S[is'c1) |s() [25°(2) 25 (1) dt, at fest (2) 13 (2) de 15*(2) 18 (2)][25"(3) 2$ (3) d?? 15² (1) 15 (1) dt, riz + r13 14 f dez - 1 223 nition of Jij by defini & Kij Jisas & Jisas + Tiszs Jis is + 2 Jisas I = *CI) 1$(2) 25(1) Q1 512) d7, riz dla 15(3)d T3 fisco) i 25" (3815 s”(1) 2513) 25 (1) 18 (3) dendte fisken? 15" (a) 23* (1) js(-) 1519) dt, dr, fiscy iscjdt, 15 (2) 15(2) d Ez =) m13 + 723 CS Seannedl withs 25 CamScanner