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[5. Heisenberg indeterminacy principle.]
Non commutative operators.
Two quantum operators u_{op} and v_{op} are called non commutative
if exists a function φ such that
u_{op} v_{op} φ ≠ v_{op} u_{op} φ .
A typical example of non commutative quantum operators is given by position and momentum operators, when
they are referred to the same axis. We have:
Assuming that p and q are referred to the same axis, this relation can be written as
Note that the notion of non commutative operators is applicable only to a pair of quantum operators:
An operator is non commutative with respect to another operators.
Two non commutative entities have different set of eigenfunctions.
