Fund Quantum Mechanics Lect & HW Solutions 89

Fund Quantum Mechanics Lect & HW Solutions 89 -...

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5.6. IDENTICAL PARTICLES 71 For ψ gs to be normalized, its square norm must be one: a ψ gs | ψ gs A = 1 . According to the previous subsection, this inner product evaluates as the sum of the inner products of the matching spin components: a a ++ ψ gs , 0 | a ++ ψ gs , 0 A + a a + ψ gs , 0 | a + ψ gs , 0 A + a a + ψ gs , 0 | a + ψ gs , 0 A + a a −− ψ gs , 0 | a −− ψ gs , 0 A = 1 Now the constants a ±± can be pulled out of the inner products as | a ±± | 2 , and the inner products that are left, all a ψ gs , 0 | ψ gs , 0 A , are one since ψ gs , 0 was normalized through the choice of the constant a . So the claimed expression results. 5.5.6 Triplet and singlet states 5.5.6.1 Solution complexse-a Question: Like the states ↑↑ , ↑↓ , ↓↑ , and ↓↓ ; the triplet and singlet states are an orthonormal
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