Aproximating a morse potential using a taylor polynomial

physicsman314

I am not going to post my question because I want to find out how to actually use the taylor polynomial and morse potential and then apply that to my problem. Say I have to approximate the morse potential using a taylor series expanding about some value. This will then find me the force constant. How would I go about setting up such equations?

Jorriss

Do you know how to taylor expand exponentials?

physicsman314

yeah, i know the formula
f(x) = f(a) + f'(a)(x-a) + f''(a)/2! (x-a)^2 and so on
I'm not sure how to do this on a morse potential. Seems like there are a lot of variables and I'm not sure from my given data, what goes where.

Jorriss

There are not more variables exactly, there are more parameters but the only independent variable is r. So try expanding in terms of r and treat everything else as a constant.