2. Consider a non-hermitian operator B and its adjoint Bt. These obey the operator relations: B² = =0 (B)2=0 BB+ B+B = 1. Define the operator N = B+B, 1 and let n) be an eigenvector of N with eigenvalue n: N|n) = n|n) i) Consider the operator N2. Write it in a form with all Bt's to the left of all B's. Simplify as much as possible. ii) Find the eigenvalues of N. Your answer from part (i) should be useful. iii) Show that B❘n) and B*|n) are both eigenvectors of N (which could be the zero vector) and find the eigenvalue in each case. iv) For what values of n is B|n) the zero vector? For what values of n is Bn) the zero vector? (hint: the zero vector has zero norm).