What Are Potential Wells in Lennard Jones Potential?

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SUMMARY

The discussion centers on the concept of potential wells in the context of Lennard-Jones potential. A potential well is defined by the equation V=0 when |x| ≥ a and V=-b when |x| ≤ a, where 'a' and 'b' are real numbers representing the parameters of the potential field. Participants clarify that at the local minimum of the potential well, kinetic energy remains non-zero, even if the potential depth 'b' approaches zero. This indicates that while particles are confined within the well, they still possess kinetic energy, challenging the notion of complete energy transition into potential energy.

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  • Understanding of Lennard-Jones potential
  • Familiarity with potential energy and kinetic energy concepts
  • Basic knowledge of mathematical functions and real numbers
  • Concept of local minima in physics
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  • Study the mathematical derivation of Lennard-Jones potential equations
  • Explore the implications of potential wells in quantum mechanics
  • Learn about energy transitions in thermodynamics
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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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