Momentum operator's relation to commutative algebra

TrickyDicky

how is the quantum momentum operator (being a linear differential op.) related to commutative algebra?

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strangerep

how is the quantum momentum operator (being a linear differential op.) related to commutative algebra?
(Linear) momentum operators corresponding to independent directions commute.

TrickyDicky

(Linear) momentum operators corresponding to independent directions commute.
Does the momentum operator by itself carry information about direction?
Or does the operator obtain it from the wavefunction?

Dickfore

how is the quantum momentum operator (being a linear differential op.) related to commutative algebra?
What commutative algebra?

dextercioby

Homework Helper
It's customary to call them Abelian algebras.