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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.

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    $\begingroup$ Can you put parentheses for what is in the product? Describe some of the degenerate cases like m=0 too. $\endgroup$ – AHusain Jul 8 '16 at 4:51
  • $\begingroup$ For m=0 it is $exp(\frac{x}{h})$ hence the operator that annihilate it is $h\frac{d}{dx}-1$. $\endgroup$ – GGT Jul 8 '16 at 7:04

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