- #1
Rettaw
- 6
- 0
Hello, I have the missfortune of having to calculate a commutator with some powers of the creation and the annihilation operators, something like:
[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?
[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?