Hi, I'm looking for a general power series for a function of F of n operators. As normal, the operators do not necessarily commute.(adsbygoogle = window.adsbygoogle || []).push({});

My first guess was:

[tex]

F(x,p) = \sum_{i=0}^\infty \sum_{j=0}^\infty a_{ij} x^i p^j + b_{ij}p^i x^j

[/tex]

However, I don't think this is correct as it is possible to have operators between x and p.

So then I thought that this might be the correct expansion:

[tex]

F(x,p) = \sum_{i=0}^\infty \sum_{j=0}^\infty a_{ij} x^i b_{ij} p^j + c_{ij} p^i d_{ij} x^j

[/tex]

Obviously, I'm just guessing here and could use some help. Why do I care about this? I am trying to derive a formula for

[F(x_1,....,x_n), G]

Suppose I know how G commutes with each of the operators x_i. I want to get an expansion for G commuting with some function F of the x_i operators. I'll work on the details of that, but first I need some help with the power series of F.

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# Power Series For Function of Operators

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