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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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It seems that at least some of the answers to your previous questions answered the question, but you have neither commented on any deficiencies in them nor accepted them. Please note that accepting answers is not only a way of acknowledging the effort people have put into answering your questions; it also serves to mark the questions as answered so that people don't keep coming back to them when looking for unanswered questions. Accepting answers is also in your own interest, since a lot of people won't answer your question when you have such a low accept rate. –  joriki Oct 19 '11 at 10:48
    
You can get a limit arrow with the $\TeX$ command \to. –  joriki Oct 19 '11 at 10:49
    
ok thanks joriki .. also, how can i 'accept' an answer as you previosly todl me in another post ?? thanks –  Jose Garcia Oct 19 '11 at 13:26
    
@Jose: Click on the tick mark just below the vote count on the answer that you want to accept. –  Hans Lundmark Oct 19 '11 at 14:01
    
@Jose: Strange, I don't remember telling you this and I can't find the comment in any of your questions -- I guess that question must have been deleted? Anyway, accepting works as Hans wrote; and you can also upvote answers (to your own questions or to others) by clicking on the up-arrow above the vote count (to the left of the answer). –  joriki Oct 19 '11 at 14:06
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