Commuting Operators: Understanding How M1,M2 & M3 Work Together

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Homework Help Overview

The discussion revolves around the properties of commuting operators, specifically ##M_1, M_2,## and ##M_3##. Participants are examining how these operators interact and the implications of their commutation in a mathematical context.

Discussion Character

  • Exploratory, Mathematical reasoning

Approaches and Questions Raised

  • Participants are attempting to understand how to manipulate expressions involving the operators, particularly focusing on rewriting terms using the commutation property of ##M_1## and ##M_2##. Questions are raised about the validity of certain transformations and the potential simplifications that can be made.

Discussion Status

The discussion is ongoing, with participants actively engaging in exploring different expressions and transformations. Some guidance has been offered regarding potential rewrites of the expressions, but no consensus has been reached on the best approach yet.

Contextual Notes

Participants are working within the constraints of the problem statement, which assumes the commutation of the operators but does not provide additional information on their specific properties or applications.

Raptor112
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Homework Statement


It is known that ##M_1,M_2, M_3## commute with each other but I don't see how the second line is achieved even though it says that it's using that ##M_1## and ##M_2## commute?
2016-04-20 (2).png
 
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Note M2(1+M1) = M2 + M2M1

How can you rewrite the right hand side using the fact that M1 and M2 commute?
 
TSny said:
Note M2(1+M1) = M2 + M2M1

How can you rewrite the right hand side using the fact that M1 and M2 commute?

##M_2 + M_1M_2##
 
Raptor112 said:
##M_2 + M_1M_2##
OK. Can you see something you can do with this expression that will help?
 
TSny said:
OK. Can you see something you can do with this expression that will help?
##(1 +M_1)M_2## ?
 
Yes.
 

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