Angular momentum commutator derivation

[asja]

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.

 

[xepma]

Hi and welcome,

L_z = x p_y - y p_x

You have it the other way around.

 

[asja]

D'oh. Thanks!