Aproximating a morse potential using a taylor polynomial

AI Thread Summary
To approximate the Morse potential using a Taylor series, the expansion should be centered around a specific value of the independent variable r. The Taylor polynomial formula can be applied, where the function f(x) is evaluated at a point a, and derivatives are computed accordingly. It is important to treat other parameters as constants during the expansion process. Clarification on the distinction between variables and parameters is essential for proper setup of the equations. Understanding these concepts will facilitate the calculation of the force constant from the Morse potential.
physicsman314
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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?
 
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physicsman314 said:
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?
Do you know how to taylor expand exponentials?
 
Jorriss said:
Do you know how to taylor expand exponentials?

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.
 
physicsman314 said:
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.
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.
 

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