2. In the above result, we say that operator r represents position and the operator in equation (5) represents momentum (in position space). All classical dynamical vari- ables can be expressed in terms of position and momentum. What we need now is a careful definition of the products of these operatos because the order in which they act is important. Using the definition of the operators in position space, (a) Calculate rpp(r) (6) (b) Calculate prý(x) (7) (c) Show that (pr – xp)v(x) = -ihw(x) (8) The resulting operation relation in equation (8) is called the commutation relation and can be expressed as [p, x] = px – xp = -ih (9) In quantum mechanics, physical variables are described by operators and these do not necessarily commute.

2. In the above result, we say that operator r represents position and the operator in equation (5) represents momentum (in position space). All classical dynamical vari- ables can be expressed in terms of position and momentum. What we need now is a careful definition of the products of these operatos because the order in which they act is important. Using the definition of the operators in position space, (a) Calculate rpp(r) (6) (b) Calculate prý(x) (7) (c) Show that (pr – xp)v(x) = -ihw(x) (8) The resulting operation relation in equation (8) is called the commutation relation and can be expressed as [p, x] = px – xp = -ih (9) In quantum mechanics, physical variables are described by operators and these do not necessarily commute.