Understanding Potential Wells: Exploring Lennard Jones Potential

[ibysaiyan]

Hi PF users,


The subject of this thread is clearly stated on the title ( above). So my question is what is mean't by a 'potential well'. I have a question based on Lennard jones potential from where this question arose in the first place ( which I will probably post on respective sub-forum if I get stumped).

My current understanding is from ( google) , someone correct me if I am mistaken but when the terms 'local minimum' are used in the context of potential well .. does it strictly imply that at this energy depth , we can't have any transition say e.g P.E into kinetic energy as it would tend to in nature (entropy).
Can someone elaborate on this.. I ask this because I have a question which's based on LJ potential equation.



Thank you.

 

[ardie]

a potential well is a potential field of the form:
V= 0 when $\left|x$$\right|$ ≥ a,
V= -b when $\left|x$$\right|$ ≤ a
i can't find the "smaller than but not equal to sign"...
ok so it looks like a well. my guess is that you are talking about the "local minimum kinetic energy" of the particle inside the well, and in that case the kinetic energy is always nonzero regardless of the size of b. i.e. even if one limits b to zero, such that you almost see that you have no potential at all, you have a finite (though infinitesimal) kinetic energy for the particle.

 

[ibysaiyan]

a potential well is a potential field of the form:
V= 0 when $\left|x$$\right|$ ≥ a,
V= -b when $\left|x$$\right|$ ≤ a
i can't find the "smaller than but not equal to sign"...
ok so it looks like a well. my guess is that you are talking about the "local minimum kinetic energy" of the particle inside the well, and in that case the kinetic energy is always nonzero regardless of the size of b. i.e. even if one limits b to zero, such that you almost see that you have no potential at all, you have a finite (though infinitesimal) kinetic energy for the particle.

Thanks for your reply but I don't think I understand the expression which you have posted above. What are the terms 'a' and 'b' above ? V I assume is the potential.

 

[ardie]

a and b can be any real number. absolutely V is the potential function which is a function of x in this instance.

 

[ibysaiyan]

a and b can be any real number. absolutely V is the potential function which is a function of x in this instance.

I see. Thanks !