brianwang writes "Michael Hall and Marcel Reginatto of the Physical-Technical Institute in Braunschweig, Germany, have published a paper with an expression that looks like Heisenberg's original relation, but gives the exact uncertainty in the measurements of position and momentum. Hall says it is an equation rather than an inequality, which is "a far stronger relation". So strong, in fact, that in a paper published this month in Journal of Physics A, have managed to derive the basics of quantum mechanics from it, including the Schrödinger equation that describes the behaviour of quantum-mechanical wave functions. http://www.newscientist.com/news/news.jsp?id=ns999 92209 It implies a tight relationship between uncertainty and energy that makes it easier to understand why, in quantum mechanics, systems have a minimum kinetic energy even if there aren't any forces acting. "There's a kind of quantum kinetic energy that comes from the uncertainty," he says. What's more, the new uncertainty equation makes it possible to estimate the minimum energy that a given quantum system should have. This is useful in cases when it's not possible to calculate the lowest energy levels precisely, particularly in complicated systems such as atoms with many orbiting electrons."