What Are Potential Wells in Lennard Jones Potential?

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Discussion Overview

The discussion centers on the concept of 'potential wells' within the context of the Lennard-Jones potential. Participants explore the definition and implications of potential wells, particularly focusing on the relationship between potential energy and kinetic energy in this framework.

Discussion Character

  • Exploratory
  • Technical explanation
  • Conceptual clarification

Main Points Raised

  • One participant seeks clarification on the term 'potential well' and its implications regarding energy transitions, particularly in relation to local minima in potential energy.
  • Another participant provides a mathematical description of a potential well, suggesting that it takes the form of a piecewise function with specific values for potential energy based on the position.
  • There is a discussion about the kinetic energy of a particle within the potential well, with one participant asserting that kinetic energy remains nonzero regardless of the potential depth.
  • Participants discuss the variables 'a' and 'b' in the potential function, with one clarifying that they can be any real numbers and that 'V' represents the potential function dependent on 'x'.

Areas of Agreement / Disagreement

Participants express varying levels of understanding regarding the definitions and implications of potential wells, with some seeking clarification while others provide explanations. No consensus is reached on the implications of local minima or the specific meanings of the variables involved.

Contextual Notes

Some participants express uncertainty about the definitions of 'a' and 'b' in the potential function, and there are unresolved questions about the implications of potential wells on energy transitions.

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

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