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

[Wan Anavan]

Homework Statement

Analysis of Angular Momentum

Relevant Equations

Commutators

is my solution correct?

 

[BvU]

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

 

[PeroK]

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.

 

[BvU]

No. Write out $L_+$ and $L_-$ and explicitly multiply

 

[Wan Anavan]

No. Write out L+L+ and L−L− and explicitly multiply

You are not being careful enough. You must write out more steps as you're going wrong with the shortcuts.

then the answer is not zero

 

[BvU]

This time answer and solution are correct.
You can check yourself by working out $\Bigl [L_+,L_-\Bigr ]$

 

[berkeman]

[ hijack ]

Two wrongs doesn't make a right

LOL. Shouldn't that be "Too wrongs doesn't make a right"?

[ /hijack ]