Morse potential


by capslock
Tags: morse, potential
capslock
capslock is offline
#1
Feb18-06, 04:53 PM
P: 17
I have the equation for the Morse potential, U = E_0 (1-exp(-a(r-r_0))^2. I'm asked to show that near the minimum of the curve the potential energy is a parabolic function. I've tried to play around with the taylor series with no hope! :( :(

Many thanks, James
Phys.Org News Partner Science news on Phys.org
Lemurs match scent of a friend to sound of her voice
Repeated self-healing now possible in composite materials
'Heartbleed' fix may slow Web performance
nrqed
nrqed is offline
#2
Feb18-06, 05:06 PM
Sci Advisor
HW Helper
P: 2,886
Quote Quote by capslock
I have the equation for the Morse potential, U = E_0 (1-exp(-a(r-r_0))^2. I'm asked to show that near the minimum of the curve the potential energy is a parabolic function. I've tried to play around with the taylor series with no hope! :( :(

Many thanks, James
It is indeed just a simple Taylor expansion! Can you show your work?
The potential vanishes at r=r_0 and the derivative of the potential also vanishes at r=r_0. The second derivative does not vanish at that point so you get that U(r) is approximately U''(r=r_0)/2 r^2 so a parabolic function.

Pat


Register to reply

Related Discussions
Morse Index Differential Geometry 4
Morse Code Programming & Computer Science 2
Morse Theory Online Calculus 11
morse code ic Electrical Engineering 3