A Simple angular momentum analysis question (check my solution please)

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The discussion revolves around verifying a solution related to angular momentum commutation relations. The initial solution contained a sign error in the commutation relations, which was later corrected. Participants emphasized the importance of careful calculations and explicitly writing out steps instead of relying on shortcuts. Ultimately, the correct answer was confirmed after thorough verification. The conversation included light-hearted banter but remained focused on the mathematical accuracy of the solution.
Wan Anavan
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Homework Statement
Analysis of Angular Momentum
Relevant Equations
Commutators
Commutators Angular Momentum.jpeg

is my solution correct?
 
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:welcome:

Not the way you write it. $$[L_x,L_y]=-i\hbar L_z$$

[edit] Sorry for confusing you. I made (a single) a sign error too !

The intention was to write $$[L_x,L_y]=\ \ \ i\hbar L_z\\ \ [L_y,L_x]=-i\hbar L_z$$

Two wrongs doesn't make a right
 
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Wan Anavan said:
Homework Statement:: Analysis of Angular Momentum
Relevant Equations:: Commutators

View attachment 261736
is my solution correct?

You are not being careful enough. You must write out more steps as you're going wrong with the shortcuts.
 
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No. Write out ##L_+## and ##L_-## and explicitly multiply
 
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BvU said:
No. Write out L+L+ and L−L− and explicitly multiply
PeroK said:
You are not being careful enough. You must write out more steps as you're going wrong with the shortcuts.
last commutation.jpeg

then the answer is not zero
 
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This time answer and solution are correct.
You can check yourself by working out ##\Bigl [L_+,L_-\Bigr ]## :wink:
 
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[ hijack ]
BvU said:
Two wrongs doesn't make a right
LOL. Shouldn't that be "Too wrongs doesn't make a right"? :wink:

[ /hijack ]
 

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