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 pq'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.