A bound quantum system has a complete set of orthonormal, no-degenerate energy eigenfunctions u(subscript n) with difference energy eigenvalues E(subscript n). The operator B-hat corresponds to some other observable and is such that:
B u(subscript 1)=u(subscript 2)
B u(subscript 2)=u(subscript 1)
B u(subscript n)=0
n>3 or B=3
Find the complete orthonormal set of eigenfunctions of the operator B-hat (expand out the eigenvectors of B in terms of u, and do not neglect any solutions)