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Angular momentum commutator derivation

  1. Sep 23, 2009 #1
    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.
     
  2. jcsd
  3. Sep 23, 2009 #2
    Hi and welcome,

    L_z = x p_y - y p_x

    You have it the other way around.
     
  4. Sep 23, 2009 #3
    D'oh. Thanks!
     
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