B. Systems of Identical Particles

Consider a system of N identical particles with hamiltonian

        H N = i=1 N p i 2 2m + i<j=1 N( N1 )/2 V( q i s i , q j s j )                  (B.1)

Indistinguishability of the particles means that H N  and all measurable quantities are invariant under permutation of the particle labels.  The eigenstates of H N  then must be representations of the permutation group.  According to the spin-statistics theorem in quantum field theory, particles with integral spins belong to the symmetric representation and are called bosons.  Particles with half-integral spins belong to the anti-symmetric representation and are called fermions. 

 

B.1.               Position and Momentum Eigenstates

B.2.               Symmetrized N-Particle Position and Momentum Eigenstates

B.3.               The Number Representation