Momentum operator's relation to commutative algebra

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

What commutative algebra?
 
It's customary to call them Abelian algebras.
 
TrickyDicky said:
Does the momentum operator by itself carry information about direction?
A (linear) momentum operator generates translations along a particular direction in space.
(I'm not sure what your background is. Normally I recommend Ballentine's textbook.)
 

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