For a Hermetian operator A, * (x)[A (x)] dx = (x)[A (x)] * dx. Assume

For a Hermetian operator Aˆ, ∫ψ^*(x)[Aˆψ (x)] dx = ∫ψ (x)[Aˆψ (x)]^*dx. Assume that Aˆ f (x) = (a + ib) f (x), where a and b are constants. Show that if Aˆ is a Hermetian operator, b = 0 so that the eigenvalues of f (x) are real.