Use the WKB approximation in the form of Equation 9.52,

to estimate the bound state energies for hydrogen. Don’t forget the centrifugal term in the effective potential (Equation 4.38). The following integral may help:

I put a prime on n', because there is no reason to suppose it corresponds to the n in the Bohr formula. Rather, it orders the states for a given ℓ, counting the number of nodes in the radial wave function. In the notation of Chapter 4, n' = N = n-ℓ (Equation 4.67). Put this in, expand the square root and compare your result to the Bohr formula.

Transcribed Image Text:

1² p(r)dr = (n' 1/2) πh (9.56)