Lecture 6

2 x1 x2 case 1 disinguishable paricles x1 x2

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Unformatted text preview: funcIon 1 [! a ( x1 )! b ( x2 ) + ! b ( x1 )! a ( x2 )] 2 1 ! " ( x1 , x2 ) = [! a ( x1 )! b ( x2 ) " ! b ( x1 )! a ( x2 )] 2 ! + ( x1 , x2 ) = Bosons Fermions We want the expectaIon value of the square of the separaIon distance between the 2 parIcles 2 < ( x1 ! x2 )2 >=< x12 > + < x2 > !2 < x1 x2 > Case 1: disInguishable parIcles ! ( x1 , x2 ) = ! a ( x1 )! b ( x2 ) < x12 >= " x12 | ! a ( x1 ) |2 dx1 " | ! b ( x2 ) |2 dx2 =< x 2 > a the exp. value of 1 parIcle x^2 " " 2 2 2 2 2 Similarly for < x2 >= | ! a ( x1 ) | dx1 x2 | ! b ( x2 ) | dx2 =< x > b < x1 x2 >= " x1 | ! ( x1 ) |2 dx1 " x2 | ! ( x2 ) |2 dx2 =< x > a < x >b 2 < ( x1 ! x2 )2 >=< x12...
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This document was uploaded on 02/04/2014.

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