For a function from a space X to itself, or for an operator that acts on such functions, rotational invariance may also mean that the function or operator commutes with rotations of X. An example is the two-dimensional Laplace operator Δ f = ∂xx f + ∂yy f: if g is the function g(p) = f(r(p)), where r is any rotation, then (Δ g)(p) = (Δ f)(r(p)) -- i.e., rotating a function merely rotates its Laplacian.
Since the rotation does not depend explicitly on time, it commutes with the energy operator. Thus for rotational invariance we must have [R, H] = 0.
Since [R, E − H] = 0, and because for infinitesimal rotations (in the xy-plane for this example; it may be done likewise for any plane) by an angle dθ the rotation operator is
in other words angular momentum is conserved.
Researchers Submit Patent Application, "Method and System for Detecting Transients in Power Grids", for Approval
Jul 11, 2013; By a News Reporter-Staff News Editor at Politics & Government Week -- From Washington, D.C., VerticalNews journalists report that...