My QM text defines the position operator as follows: The position operator $X= (X_1,X_2,X_3)$ is such that for $j=1,2,3: \ X_j \psi(x,y,z)= x_j \psi(x,y,z)$. To me this can mean two things. 1) $X$ is a vector and acts as $X \psi(x,y,z)= (x \psi(x,y,z), y \psi(x,y,z), z \psi(x,y,z))$. But...