Quantum Engi Q and A_Part_24

Quantum Engi Q and A_Part_24 - 70 CHAPTER 5....

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Unformatted text preview: 70 CHAPTER 5. MULTIPLE-PARTICLE SYSTEMS This is similar to the observation in calculus that integrals of products can be factored into separate integrals: integraldisplay all vectorr 1 integraldisplay all vectorr 2 f ( vectorr 1 ) g ( vectorr 2 ) d 3 vectorr 1 d 3 vectorr 2 = bracketleftbiggintegraldisplay all vectorr 1 f ( vectorr 1 ) d 3 vectorr 1 bracketrightbiggbracketleftbiggintegraldisplay all vectorr 2 g ( vectorr 2 ) d 3 vectorr 2 bracketrightbigg Answer: (|)(|) = summationdisplay S z 1 = 1 2 h ( S z 1 ) ( S z 1 ) summationdisplay S z 2 = 1 2 h ( S z 2 ) ( S z 2 ) and written out (|)(|) = bracketleftBig (+ 1 2 h ) (+ 1 2 h ) + ( 1 2 h ) ( 1 2 h ) bracketrightBigbracketleftBig (+ 1 2 h ) (+ 1 2 h ) + ( 1 2 h ) ( 1 2 h ) bracketrightBig 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, (|) = (+ 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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This note was uploaded on 11/13/2011 for the course PHY 4458 taught by Professor Garvin during the Fall '11 term at University of Florida.

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Quantum Engi Q and A_Part_24 - 70 CHAPTER 5....

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