Simplify ladder operators



Hi all,

> An analogous technique for simplifying trigonometric expressions is
> to convert them all to complex exponentials and then treat them as
> rational functions in
> 
> y=exp(ix)   where x is appropriately chosen to be the least common 
> multiple of all imaginary exponents.
> 
> Then rationally simplify the result, which is a ratio of polynomials
> in y.
> 
> This replaces all the "rules" you know about half angles etc with a 
> uniform procedure.
> 
> I do not know if there is some canonical transformation for the 
> expressions of interest here, but if there is one,
> consider using it.

Sure this general procedure is the better approach. But I don't know
how this could work here. I even don't know a canonical form for the
operator expressions.

Any hint is welcome.


-- Raoul