2) a) Determine the adjoint operator to â = c + id, where c and d are real numbers and i = √-1. Is â Hermitian? b) If  is a Hermitian operator, then *  dx = f(Â) dx for wave functions and (optional proof available in Moodle in section 2). Using this relation, show that the eigenfunctions of a Hermitian operator  are orthogonal provided that they have different eigenvalues. Explain the significance of this result.

Fig: 1