Occupation Number Representation

Occupation number representation is introduced in terms of single particle creation and annihilation operators, satisfying boson (or fermion) commutation (or anti-commutation) relations, for a many-boson (or many-fermion) system. Incorporation of symmetrization or antisymmetrization of wave function becomes simple. Representation of one-body and two-body operators and calculation of their matrix elements have been discussed for both bosonic and fermionic systems. Wick’s theorem is stated and its use demonstrated in evaluation of matrix elements.