# boundary conditions

Consider the following operator: $-i\hbar x\frac{df(x)}{dx}-i\hbar \frac{f(x)}{2}=E_{n}f(x)$

What kind of boundary conditions can I enforce? I have tried to find a function such that for every integer $n$ I get $f(nx)=f(x)$, but I only get that $f(x)$ must be a constant.

Of course I know how to solve it to get the solution $f(x)= \frac{C}{x^{1/2-iE_{n}}}$

or perhaps to set the conditions $F(nx)=F(x)$ for every integer $n$ with given

$F(x)= \sum_{p} \sum_{k=-\infty}^{\infty}f(p^{k}x)$ with $f(x)$ solving the above equation and 'p' runs over the primes $p=2,3,5,7,11,...$

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No offense, but this sort of sounds like a homework problem. Is it? – Colin Fredericks Jun 1 '12 at 18:40
no, it isn't i have a degree on physics :) (although i am currently unemployed) i was looking for a solution of this strange problem :S – Jose Javier Garcia Jun 1 '12 at 19:02
@JoseJavierGarcia: FYI, it doesn't matter if it was assigned as actual homework or not to qualify as homework under the SE rules. – JamalS Dec 18 '14 at 11:04