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edited Nov 18, 2016 at 1:20

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Binomial expansion for non commutativenoncommutative operator

How can I writeIs it possible to find a closed formula for $(A^\dagger -kA)^n$ with $[A,A^\dagger]=1$ ?

I lookam looking for the normal ordinate form: $\sum (A)^(n-j)(A^\dagger)^j$ maybe plus$\sum (A)^{n-j}(A^\dagger)^j$— possibly something to do with the commutator, I don't know.

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asked Nov 17, 2016 at 22:07

Flávio Oliveira Neto

Binomial expansion for non commutative operator

How can I write a closed formula for $(A^\dagger -kA)^n$ with $[A,A^\dagger]=1$ ?

I look for the normal ordinate form: $\sum (A)^(n-j)(A^\dagger)^j$ maybe plus something to do with the commutator, I don't know.

noncommutative-algebra binomial-coefficients

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Binomial expansion for non commutativenoncommutative operator

Binomial expansion for non commutative operator

Binomial expansion for noncommutative operator

Binomial expansion for non commutative operator