Semiclassical approach

funduk89

1. The problem statement, all variables and given/known data

I have potential hole from a to b. This potential hole is sum of U(r) (bounded function) and l(l+1)/r^2, where l is azimuthal quantum number. In my book about semiclassical approach is written: if [tex]n_{r}[/tex] >>1 then in rules of quantization in basic range of integration centrifugal potential is correct with order of magnitude is
[tex]\frac{(l+1/2)^{2}}{n^{2}_{r}}[/tex]. I cant undrstand, why it so

2. Relevant equations

[tex]\int\sqrt{2(E-U(r)-\frac{l(l+1)}{2r^{2}})}[/tex] = [tex]n_{r}[/tex]+[tex]\gamma[/tex] Bohr's rules of quantization

[tex]\frac{l(l+1)}{2r^{2}}[/tex] centrifugal potential


3. The attempt at a solution
I try to prove it so: i investigate difference between two integrals: one of them include centrifugal potential, other no. But i cant obtain this formula. I am sure, this formula obtain very easy, but i dont no how. Have you got any ideas?

P.S sorry my english