I have the following function in $x$. $\sum_{d=0}^{\infty} \frac{1}{\hbar^d}\frac{1}{d!}\left(\prod_{i=1}^{d-1}(1+i\hbar)^{m}\right)x^d$
I need a differential operator involving $(x,\frac{d}{dx},h,m)$ that is can be a polynomial in this 4 terms such that it annihilates the wave function. Or can give a proof that there does not exist such operator. I feel that there should be one.