Wednesday, April 10, 2013

Another look at the Schroedinger equation

I just read this article on PhysOrg about a paper recently published on the origins of the Schroedinger equation. One interesting thing I learned is that, in the classical wave equation for matter waves, the phase of the wave determines the amplitude. However, in Schroedinger's equation, the amplitude and phase of the wave are coupled to one another.

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?