P21.6 The operator for the square of the total spin of two electrons is Stotal = (S₁ + S₂)² = S² + S² + 2(S1xS2x + S1yS2y + $1$22). Given that Sα =B₁ 2 S,B= iħ S,α =B₁ Ŝ₂α 2 = = 九↓2 ħ α, ħ iħ ħ α, Syß α₁ S₂B = 1/- B₁ a, 2 2 2 show that a (1) a (2) and ß (1) ß (2) are eigenfunctions of the operator Stotal. What is the eigenvalue in each case?
P21.6 The operator for the square of the total spin of two electrons is Stotal = (S₁ + S₂)² = S² + S² + 2(S1xS2x + S1yS2y + $1$22). Given that Sα =B₁ 2 S,B= iħ S,α =B₁ Ŝ₂α 2 = = 九↓2 ħ α, ħ iħ ħ α, Syß α₁ S₂B = 1/- B₁ a, 2 2 2 show that a (1) a (2) and ß (1) ß (2) are eigenfunctions of the operator Stotal. What is the eigenvalue in each case?
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Transcribed Image Text:P21.6 The operator for the square of the total spin of two
electrons is Stotal = (S₁ + S₂)² = S² + S² +
2(S1xS2x + S1yS2y + $1$22). Given that
iħ
S₁α = /B₁ S₁,α = 22²1
2
SxB
=
ħ
2
α,
B, S₂α
=
=
九↓2
ħ
α,
iħ
ħ
S,ß α₁ S₂B = 1/- B₁
a,
2
2
show that a (1) a (2) and ß (1) ß (2) are eigenfunctions of
the operator Stotal. What is the eigenvalue in each case?
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