Mauro Murzi's pages on Philosophy of Science - Quantum mechanics
Non commutative operators
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[5. Heisenberg indeterminacy principle.]

Non commutative operators.

Two quantum operators uop and vop are called non commutative if exists a function φ such that uop vop φ ≠ vop uop 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:

Non commutative operators

Assuming that p and q are referred to the same axis, this relation can be written as

General formula for non commutative operators

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.

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