In this problem you will supply the missing steps in the derivation of the formula E_singlet= E_1s+ E_2s+ J + K for the singlet level of the 1s¹2s¹configuration of He.

a. Expand Equation (22.17) to obtain

b. Starting from the equations 1 2 Hˆ i1s(i) = E s1s(i) and Hˆ i 2s(i) = E s 2s(i), show that

c. Expand the previous equation using the definitions

to obtain the desired result, Esinglet = E_1s + E_2s + J + K.

Transcribed Image Text:

1 [[ls(1)2s (2) + 2s (1) Is (2)](H1) [1s (1) 2s (2) + 2s (1) ls (2)]dT¡dr2 Esinglet [ls(1)2s (2) + 2s (1) Is (2)](Ĥ2) [1s (1) 2s (2) + 2s (1) 1s (2)]dT¡dr2 S/ [1s (1) 2s (2) + 2s (1) 1s (2)] × 121(2) 4πεο Γ-1 , [1s (1) 2s (2) + 2s (1) ls (2)]dr¡dr2 singlet = E + E. jus02C)- [Ls1)25(2) + 25(1)ls(2)]| 4πεο μ-2) [1s (1) 2s (2) + 2s (1)1s(2)] d, dr,