# boundary conditions

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

what kind of bundary conditions can i put ?? i have tried to find a function so 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
Ok! Just wanted to make sure. Thanks! –  Colin Fredericks Jun 1 '12 at 19:10