  We apply the Walborn [Walborn S P, Taketani B G, Salles A, Toscano F and de
Matos Filho R L 2009 Entropic Entanglement Criteria for Continuous Variables
Phys. Rev. Lett. 103 160505] Shannon Entropic Entanglement Criterion (SEEC), to
simple harmonic oscillators, a system typically discussed in undergraduate
quantum mechanics courses. In particular, we investigate the entanglement of a
system of coupled harmonic oscillators. A simple form of entanglement criterion
in terms of their interaction is found. It is shown that a pair of interacting
ground state coupled oscillators are more likely to be entangled for weaker
coupling strengths while coupled oscillators in excited states entangle at
higher coupling strengths. Interacting oscillators are more likely to be
entangled as their interaction increases.
