In an exercise, I was given the following Lagrangian: $$L=\frac{m}{2}\sum_{j=1}^{N}\dot{q}_j^2-\sum_{j=1}^{N-1}V(q_{j+1}-q_j),$$ where $$V(r)=\frac{A}{6}r^{-6}+\frac{B}{3}r^{-3}.$$ What kind of physical system could it represent? Is there any serious study/application for this system?
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2$\begingroup$ Lennard-Jones potential. $\endgroup$– AccidentalFourierTransformCommented Apr 26, 2018 at 23:16
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$\begingroup$ @AccidentalFourierTransform do you know of examples involving more than pairs of atoms? $\endgroup$– ZeroTheHeroCommented Apr 26, 2018 at 23:45
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$\begingroup$ Hey! @DanielSank, why do you do that? This is not my question. I want to know about physical explanation. Not about how write a Lagrangian. With the title you put in my question you miss my point. $\endgroup$– Ernesto IglesiasCommented Apr 26, 2018 at 23:49
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$\begingroup$ @ErnestoIglesias The new title asks exactly what you write in your comment. I do not understand your complaint. $\endgroup$– DanielSankCommented Apr 26, 2018 at 23:51
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1$\begingroup$ Yes, mine missed the point, but the original one conveyed basically nothing and misused the word "why". Anyway, the most recent one looks quite nice. $\endgroup$– DanielSankCommented Apr 27, 2018 at 0:45
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1 Answer
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van der Waals potential could decay in $1/r^6$, dipole-dipole interaction potential could decay in the form of $1/r^3$. This is probably related to the inter molecular interaction.
