# eigenvalue problem

let be the 2 eignevalue problems

1. $-y''(x)+f(x)y(x)=E_{n}y(x)$ with the boundary condition $y(0)=0= y(L)$

2. $-y''(x)+g(x)y(x)=\lambda _{n}y(x)$ with the boundary condition $y(0)=0= y(L)$

here L is a real number , we can also have $L= \infty$

then if for big $x$, $x\to \infty$ we have that the quotient $\frac{f(x)}{g(x)}=1$

then does it mean that $\frac{E_{n}}{\lambda_{n}}=1$ in the limit $n\to\infty$ ? for the eigenvalues ??

using the WKB approximation i believe that my assertion is true however i can not prove it.. thanks in advance

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You can get a limit arrow with the $\TeX$ command \to. –  joriki Oct 19 '11 at 10:49