Angular momentum commutator derivation

  • Thread starter asja
  • Start date
  • #1
4
0
I am trying to prove:
L_xL_y - LyLx = ihL_z

Unfortunately I keep getting L_xL_y - L_yL_x = -ihL_z and I was hoping someone could spot the error in my calculations:

L_xL_y - L_yL_x = ( yp_z - zp_y )( zp_x - xp_z ) - ( zp_x - xp_z )( yp_z - zp_y )
= yp_zzp_x - yp_zxp_z - zp_yzp_x + zp_yxp_z - zp_xyp_z + zp_xzp_y + xp_zyp_z - xp_zzp_y
= p_zz( yp_x - xp_y ) + zp_z( p_yx - p_xy )
= p_zzL_z - zp_zL_z
= L_z( p_zz - zp_z )
= -ihL_z

Thanks for any help.
 

Answers and Replies

  • #2
525
7
Hi and welcome,

L_z = x p_y - y p_x

You have it the other way around.
 
  • #3
4
0
D'oh. Thanks!
 

Related Threads on Angular momentum commutator derivation

Replies
5
Views
7K
  • Last Post
Replies
3
Views
851
Replies
5
Views
1K
Replies
3
Views
5K
Replies
6
Views
3K
  • Last Post
Replies
3
Views
655
Replies
5
Views
702
Replies
10
Views
3K
Replies
0
Views
116
Replies
5
Views
1K
Top