Because the operators X and P are not compatible, 
, there is no
measurement that can precisely determine both X and P simultaneously.
Hence, there must be an uncertainty relation between them that specifies how
uncertain we are about one quantity given a definite precision in the measurement
of the other. Presumably, if one can be determined with infinite precision, then
there will be an infinite uncertainty in the other. Recall that we had
defined the uncertainty in a quantity by
Thus, for X and P, we have
These quantities can be expressed explicitly in terms of the wave
function 
using the fact that
and
Similarly,
and
Then, the Heisenberg uncertainty principle states that
which essentially states that the greater certainty with which a measurement of X or P can be made, the greater will be the uncertainty in the other.