In quantum mechanics, physical observables that are scalars, vectors, and tensors, must be represented by scalar, vector, and tensor operators, respectively. Whether something is a scalar, vector, or tensor depends on how it is viewed by two observers whose coordinate frames are related to each other by a rotation. Alternatively, one may ask how, for a single observer, a physical quantity transforms if the state of the system is rotated. Consider, for example, a system consisting of a molecule of mass M , traveling with a definite center of mass momentum, p z ^ ^ , in the z direction. If we rotate the system by 90 ∘ ∘ about the y axis, the momentum will change to p x ^ ^ , which is in the x direction. The center-of-mass kinetic energy of the molecule will, however, be unchanged at p 2 / 2 M . The kinetic energy is a scalar and the momentum is a vector, and these two quantities must be represented by a scalar and a vector operator, respectively. By the latter in particular, we mean an operator whose expected values in the initial and the rotated states are p z ^ ^ and p x ^ ^ . The kinetic energy on the other hand must be represented by a scalar operator, whose expected value must be the same in the initial and the rotated states.