In a typical introductory course on quantum mechanics the student has to face two quite different
operator products. One of them leads to, for example, commutators and the uncertainty principle, and
the other appears when one goes from a one-particle system to a multi-particle one. The latter gives
rise to the direct or tensor product of operators and vector spaces, and to the Kronecker product of
the matrix representations of the operators. We illustrate the practical utility of the Kronecker
product by means of two spin systems commonly discussed in introductory courses on quantum mechanics
and also by means of a simple model for the interpretation of the NMR signal produced by two
interacting protons.