Finding the commutator [x, l²] in quantum mechanics

[mudyos]

Hi

I can not Continues Solution because of the differentiate .

please

I want Some the helping and Exposition .

see a file attach

 

[mudyos]

Solution please

 

[malawi_glenn]

Skip the derivatives, you where on the right way by writing $$\hat{\vec{L}}$$ as $$\hat{L}_x^2 + ..$$ and using the commutator rules and the commutators $$[x,\hat{L}_x]$$ etc.

Hint: Use the fact that you can write $$\hat{L}_z = x\hat{p}_y - y\hat{p}_x$$ etc, and $$[x_i,\hat{p}_j] = i\hbar \delta _{i,j}$$ ; where $$\vec{x} = x,y,z$$. So $$x_i$$ can be either x,y,z.

Much work ;)

Dont demand solutions from us, we only give you hints and point you in the right direction. That is also a rule, that full solutions shoulnd be posted. We would also be sitting approx 45min to do this, and it is not us who should do the work, it is you, we only give hints as I said.

Now you have everything to solve this.