Problem. Is (1,2)-1s(1)(1)Is(2)(2) +1s(2)(2)Is(1)(1) an eigenfuntion of5,?Ifit i

Question

Problem. Is (1,2)-1s(1)(1)Is(2)(2) +1s(2)(2)Is(1)(1) an eigenfuntion of5,?Ifit is, what is MS? Answer. Before pursuing this problem, it is helpful to notice that can be written as a product of spatial and spin func- tions: (1,2)= ls(1)1s(2)[a(1)(2)+(2)(1)] Spin operators work on spin functions only, so we can ignore the spatial functions. We only need to determine whether the spin function is an eigenfunction of the spin operator. Engel, eq. 10.23 (p. 195) states S 32.The latter operators work on one-electron spin functions only and ignore the spin functions of other electrons. The rules for working with these operators are given in Engel, eq. 104. (p. 182). hbar 3,1 [a(1) (2) + (2) (1)] = [+(1) (2)-(2) (1)] Sz2 Adding gives these results together is an eigenfunction of the operator with eigenvalue-0. MS = 0.

Explanation / Answer

Its not the alphas. The sighns are for the whole term. See doing this type of problems we use linear combination and for doing linear combination we have 2 options one is plus one is minus. Again see electrons have spins up and down ,for up we use positive sign and for down spin we use negativve sign. Thats why those signs are coming it is mainly due to the rule of linear combination

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