Lecture 5 part2

create a permutaon operator that switches the

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: ching coordinates cannot change the overall energy of the system, otherwise you could tell them apart.) •  Create a permuta?on operator that switches the variables of par?cles i and j. [ Pi , j , H ] = 0 Pi , j! (q1 , ...qi , ...q j , ...qN ) = ! (q1 , ...q j , ...qi , ...qN ) If ! (q1 , ...qi , ...q j , ...qN ) is an eigenfunc?on of H with eigenvalue E, so is Pi , j! 2 Applying P twice brings us back to the ini?al configura?on: Pi , j = I Eigenvalues are therefore ! = ±1 Indis?nguishable par?cles •  The wavefunc?ons corresponding to eigenvalue +ε: Pi , j! (q1 , ...qi , ...q j , ...qN ) = ! (q1 , ...q j , ...qi , ...qN )...
View Full Document

This document was uploaded on 02/04/2014.

Ask a homework question - tutors are online