Hello, I have the missfortune of having to calculate a commutator with some powers of the creation and the annihilation operators, something like:(adsbygoogle = window.adsbygoogle || []).push({});

[tex] \left[ a^m , (a^{\dagger})^n \right][/tex]

I have managed to derive

[tex] \left[ a^m , (a^{\dagger})^n \right]= m a^{m-1} \left[ a , a^{\dagger} \right] [/tex]

(altought I should really have remebered that) but I don't know how to use that to calculate

the big thing other than by recursive application of it, and that's very messy.

Any suggestions?

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# Commuting creation and annihilation operators

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