commutation of operators


by solas99
Tags: commutation, operators
solas99
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#1
Jan15-12, 03:50 PM
P: 69
what is the physical significance of the commutation of operators?
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tom.stoer
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#2
Jan15-12, 04:59 PM
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One can e.g. derive the Heisenberg uncertainty principle
lpetrich
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#3
Jan15-12, 06:15 PM
P: 512
An interpretation of operators' commutator is what happens when those operators' operations interfere with each other. This interference is what leads to the Uncertainty Principle.

Like position and momentum operators. These operators measure those quantities, and attempting to do so for the same direction of position and momentum leads to interference. However, position and momentum in orthogonal directions do not interfere with each other.

jfy4
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#4
Jan15-12, 10:58 PM
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P: 647

commutation of operators


another snazzy way to think about them is as indicators for "curvature". Since it suits a lot of people to think about physics as geometry, the commutation of operators can be used to see the curvature, more or less, of the "space" of states.
ibysaiyan
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#5
Jan16-12, 05:23 AM
P: 437
Quote Quote by lpetrich View Post
An interpretation of operators' commutator is what happens when those operators' operations interfere with each other. This interference is what leads to the Uncertainty Principle.

Like position and momentum operators. These operators measure those quantities, and attempting to do so for the same direction of position and momentum leads to interference. However, position and momentum in orthogonal directions do not interfere with each other.
So basically we can infer either of the two quantities due to the commutative nature of the operators.Provided, they happen in the same direction , am I right to think it this way ?


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