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This isn't really a homework question, it came along in my studying of the chapter, but it is a homework "type" question so I assumed this would be the best place to post this.

I am trying to show that

[tex][L_x,L_y]=y[p_z,z]p_x+x[z,p_z]p_y=i \hbar L_z[/tex]

This is all the work the book showed. So I tried to come to this conclusion myself and it is proving to be more difficult than I had originally thought. So here is what I did..

Here are the commutator properties I used..

http://imageshack.us/a/img823/9923/proby1l.png [Broken]

And here is my work using those properties..

http://imageshack.us/a/img441/8048/proby2.png [Broken]

My question is, is there an easier way to do this? Also, how in the hell does that big block of terms simplify to those two terms? It looks like the first and last term in that whole mess are the only ones that survive somehow.

Can anyone help?

I am trying to show that

[tex][L_x,L_y]=y[p_z,z]p_x+x[z,p_z]p_y=i \hbar L_z[/tex]

This is all the work the book showed. So I tried to come to this conclusion myself and it is proving to be more difficult than I had originally thought. So here is what I did..

Here are the commutator properties I used..

http://imageshack.us/a/img823/9923/proby1l.png [Broken]

And here is my work using those properties..

http://imageshack.us/a/img441/8048/proby2.png [Broken]

My question is, is there an easier way to do this? Also, how in the hell does that big block of terms simplify to those two terms? It looks like the first and last term in that whole mess are the only ones that survive somehow.

Can anyone help?

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