We apply the linear momentum operator to each of the given functions:
$\begin{align*}(A)& \frac{\hbar}{i} \frac{\partial}{\partial x} \cos(k x) = i \hbar k \sin (k x) \\(B)& \frac{\hbar}{i...$
So, (A) and (B) are not even eigenfunctions of the linear momentum operator. (C), (D), and (E) are all eigenfunctions of the linear momentum operator, but the eigenvalue of (C) is $- \hbar k$ and the eigenvalue of (E) is $k i$ . The eigenvalue of (D) is $\hbar k$ , so the correct answer is (D).

Solution to 1986 Problem 57