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quantum mechanics - Binomial expansion of non-commutative operators - Physics Stack Exchange

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Stack Exchange network consists of 183 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers. Ask questions, find answers and collaborate at work with Stack Overflow for Teams. Ask questions, find answers and collaborate at work with Stack Overflow for Teams. Explore Teams Teams Q&A for work Connect and share knowledge within a single location that is structured and easy to search. I would like to determine the general expansion of ( 𝐴 ̂  + 𝐵 ̂  ) 𝑛 , ( 𝐴 ^ + 𝐵 ^ ) 𝑛 , where [ 𝐴 ̂  , 𝐵 ̂  ]≠0 [ 𝐴 ^ , 𝐵 ^ ] ≠ 0 , i.e. 𝐴 ̂  𝐴 ^ and 𝐵 ̂  𝐵 ^ are two generally non-commutative operators. How could I express this in terms of summations of the products of 𝐴 ̂  𝐴 ^ and 𝐵 ̂  𝐵 ^ operators? I would like to determine the general expansion of (𝐴+𝐵 ) 𝑛 ( 𝐴 + 𝐵 ) 𝑛 , where [A,B]≠0 The expansion of (𝐴+𝐵 ) 𝑛 ( 𝐴 + 𝐵 ) 𝑛 for non-commuti

quantum mechanics - Binomial expansion of non-commutative operators - Physics Stack Exchange Stack Internal Knowledge at work Bring the best of human thought and AI automation together at your work. Explore Stack Internal Binomial expansion of non-commutative operators Ask Question Asked 11 years, 2 months ago Modified 4 years, 3 months ago Viewed 13k times 16 $\begingroup$ I would like to determine the general expansion of $$(\hat{A}+\hat{B})^n,$$ where $[\hat{A},\hat{B}]\neq 0$ , i.e. $\hat{A}$ and $\hat{B}$ are two generally non-commutative operators. How could I express this in terms of su

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