E The Occupation Number Representation

This equation shows that the function a ng. ..n. .. is an eigenfunction of the operator a a which belongs to the eigenvalue + 1 and as such must be proportional to jn. ..n + 1. .. . We write therefore 

The normalization factors N (n- ) and N (n ) are determined from the orthogonality condition (2.107) 

From these equations, we immediately obtain the individual matrix elements n a ns = (n3 + l) n, n +1 ( -13) 

However, due to the orthogonality of the wave functions (2.107), the above brackets are zero and we obtain the result 

---