The authors of the PNAS article demonstrate that this coupling leads to the linearity of the Schroedinger equation, which is one of its most important properties. If it were not linear, I'm not sure that the mathematics would have turned out so relatively simple in quantum mechanics; i.e. it may not have been formulated in terms of linear algebra.

Unfortunately, I think the PhysOrg article was a bit misleading. They repeatedly referred to the classical wave equation when speaking of the Hamilton-Jacobi equation. To my knowledge, the classical wave equation and the HJ equation describe different things. More importantly, the classical wave equation

*is*linear.

Is it better to be absolutely truthful in popular science articles or to minimize the amount of jargon and smooth over some minute but important points?