Lennard Jones Potential & Kinetic Energy

[relskhan]

So I'm trying to model two particle interaction subject only to Lennard Jones potential. I have a specific potential I am using:

My problem is forcing the two particles into the potential well. I have the particles at a separation distance of 2.5*10^-8. The way I interpret this potential is that I can set a total energy of -6.0*10^-20 by giving the particles a Kinetic Energy of 3.95*10^-20 (Where Total Energy TE=KE + U or KE = TE - U => KE = -6.0*10^-20 +9.95*10^-20 = 3.95*10^-20 , the -9.95*10^-20 comes from U(2.5*10^-8).

To set the kinetic energy I'm using 1/2 m (v1²+v2²). And giving particle 1 an initial velocity equal to some factor of particle 2's velocity.

Unfortunately, this is still not working. So I am either interpreting the different energy requirements on the diagram wrong - or not calculating the velocity for the KE correctly. Any ideas??

 

[UVCatastrophe]

How many dimensions? In dimensions higher than 1 you'll need a centrifugal term.

Actually, I'm not sure if this answers your question.

 

[relskhan]

How many dimensions? In dimensions higher than 1 you'll need a centrifugal term.

Actually, I'm not sure if this answers your question.

Good Point - I should have specified. This is all 1-D, I will 'upscale' to 3-D later, but for now, I just want the simplest model.

 

[Calion]

What isn't working about it? It might be easier to work out in an inertial frame where one particle has 0 velocity.

 

[relskhan]

What isn't working about it? It might be easier to work out in an inertial frame where one particle has 0 velocity.

Well I didn't want to get into the details too far - I mostly want to make sure my interpretation of the Energies are correct. I could try starting the particle at 0 velocity - but - the potential will move it I'm sure.