You might have heard of commuting and non commuting operators. What do they mean?

If , then we say that the operators *Â* and *B* do not commute. The corresponding physical observables *A* and *B* are then said to be complementary observables.

The quantity is expressed as [*Â*,*B*] and called the commutator of the operators *Â* and *B*.

So when two operators do not commute

and when two operators do commute

In particular, quantum mechanical operators are postulated to satisfy the following commutation relations:

The *q's* are the cartesian coordinates and the *p*_{q}'*s* are the corresponding conjugate momenta. Needless to mention, they are a set of complementary observables and as we shall see soon, obey Heisenberg's uncertainty principle.

2007-09-27