Lecture 6

A x1 2 dx1 b x2 2 dx2 x12 b x1 2

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Unformatted text preview: > + < x2 > !2 < x1 x2 > =< x 2 > a + < x 2 >b !2 < x > a < x >b so if parIcle 1 is at x= ­1 and parIcle 2 is at x=2 then the square of the distance b/w them is 3^2 (as expected!) Case 2: IdenIcal parIcles 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 2 < ( x1 ! x2 )2 >=< x12 > + < x2 > !2 < x1 x2 > 1# 2 x1 | ! a ( x1 ) |2 dx1 " | ! b ( x2 ) |2 dx2 + " x12 | ! b ( x1 ) |2 dx1 " | ! a ( x2 ) |2 dx2 2 $" ± " x12! a ( x1 )*! b ( x1 ) dx1 " ! b ( x2 )*! a ( x2 ) dx2 ± " x12! b ( x1 )*! a ( x1 ) dx1 " ! a ( x2 )*! b ( x2 ) dx2 < x12 >= Boaom two terms are =0 b/c states are or...
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This document was uploaded on 02/04/2014.

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