(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

in the first part of the problem we were told to estimate the lowest energy of a electron in a hydrogen atom for a certain orbital angular momentum l by evaluating the equation for effective potential at it's minimum. That is to say that for any given l the minimum energy state has n = l + 1. If you then evaluate V-eff = l(l+1)/2p^2 -1/p for l = n - 1 and p=p0=l(l+1) this should be a rough estimate of the actual energy. Now this is easy enough to evaluate and gives not too large of an overestimate; the next part of the problem, however, has me a little confused. For the same case I'm supposed improve the estimate by making a second order taylor expansion of V-eff about p0. The thing is I really don't see how a taylor expansion is supposed to help me, especially considering that the value at p0 will be no different than that of the original function.

2. Relevant equations

V-eff = l(l+1)/2p^2 -1/p

exact energy eigenvalues = [tex]\lambda[/tex]n = 1/(2n^2), n = 1, 2, 3, ...

3. The attempt at a solution

Finding the taylor series is simple enough, giving you

(n^2-n-p)^2/(n*(n-1))^3 - 1 /(2n*(n-1))

The problem is that I don't know what to do with this now that I have it.

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Energy level approximation

Can you offer guidance or do you also need help?

Draft saved
Draft deleted

**Physics Forums | Science Articles, Homework Help, Discussion**