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Unformatted text preview: 3. An operator A( λ ) , which depends explicitly on a continuous parameter , is said to be differentiable if d A d A d dA d ) ( ) ( lim − + = ∞ → exists. (a) if two operators A and B are differentiable, show that λλ d dB A B d dA AB d d + = ) ( (b) if A is differentiable and has its inverse, show that 1 1 1 − − − − = A d dA A d dA 4. For any operators A and B, and for a real parameter , prove that exp( λ B)A exp(-λ B)=A+i λ [B, A] - λ 2 /2[B,[B,A]]+… , where the nth term is ]]]] , [ , [ , [ , [ ! 1 A B B B B i n n n L . This is the Baker-Hausdorff lemma....
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This note was uploaded on 10/11/2009 for the course PHYSICS 866 taught by Professor Js during the Spring '08 term at Pohang University of Science and Technology.
- Spring '08