VIRIAL THEOREM AND SCALE TRANSFORMATIONS

In this article the virial theorem, which is useful in classical, quantum, and statistical mechanics, is considered. Most derivations of this result are of one of two types. Either one starts with the function r-p [or operator 1/2 (r.p + p-r)], or else takes a derivative with respect to the parameter of a scale transformation. It is pointed out that these two methods are closely related, since r.p [or 1/2 (r.p + P.r)] is the generator of scale transformations. This is demonstrated explicitly for classical and quantum-mechanical systems. The pedagogical advantages in pointing out this connection are also examined. © 1979, American Association of Physics Teachers. All rights reserved.