Fund Quantum Mechanics Lect &amp; HW Solutions 88

# Fund Quantum Mechanics Lect &amp; HW Solutions 88 - 70...

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70 CHAPTER 5. MULTIPLE-PARTICLE SYSTEMS This is similar to the observation in calculus that integrals of products can be factored into separate integrals: i all vr 1 i all vr 2 f ( vr 1 ) g ( vr 2 ) d 3 vr 1 d 3 vr 2 = bi all vr 1 f ( vr 1 ) d 3 vr 1 Bbi all vr 2 g ( vr 2 ) d 3 vr 2 B Answer: a↑|↓Aa↑|↑A = s S z 1 = ± 1 2 ¯ h ( S z 1 ) ( S z 1 ) s S z 2 = ± 1 2 ¯ h ( S z 2 ) ( S z 2 ) and written out a↑|↓Aa↑|↑A = ± (+ 1 2 ¯ h ) (+ 1 2 ¯ h ) + ( 1 2 ¯ h ) ( 1 2 ¯ h ) ²± (+ 1 2 ¯ h ) (+ 1 2 ¯ h ) + ( 1 2 ¯ h ) ( 1 2 ¯ h ) ² and multiplying out, and reordering the second and third factor in each term, you see it is the same as the expression obtained in the answer to the previous question, a↑↑|↓↑A = (+ 1 2 ¯ h ) (+ 1 2 ¯ h ) (+ 1 2 ¯ h ) (+ 1 2 ¯ h ) + (+ 1 2 ¯ h ) ( 1 2 ¯ h ) (+ 1 2 ¯ h ) ( 1 2 ¯ h ) + ( 1 2 ¯ h ) (+ 1 2 ¯ h ) ( 1
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