1. May 3, 2005 #1

   S.G.

   

   How do you prove the following identity for non-commuting operators A and B?
   
   [[[A,B],B]A]=[B,[A,[A,B]]]

    

   S.G., May 3, 2005
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3. May 3, 2005 #2

   Edgardo

   

   Hello S.G.,
   
   you could first use the abbreviation C:= [A,B], so the equation
   looks better:
   
   [[[A,B],B]A]=[B,[A,[A,B]]]
   <=>
   [[C,B],A] = [B,[A,C]]
   
   Then use the definition of the commutator [Y,Z] = YZ-ZY
   and in the end, instead of C, use [A,B] again.

    

   Edgardo, May 3, 2005

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