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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.

Commutative operators

The effect of measurement on Ψ-function