# Semiclassical approach

1. Mar 10, 2010

### 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 $$n_{r}$$ >>1 then in rules of quantization in basic range of integration centrifugal potential is correct with order of magnitude is
$$\frac{(l+1/2)^{2}}{n^{2}_{r}}$$. I cant undrstand, why it so

2. Relevant equations

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

$$\frac{l(l+1)}{2r^{2}}$$ 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

Last edited: Mar 11, 2010