# Tag Info

1

This is wholly analogous to the evanescent optical field that arises in the classically (i.e. computed by raytracing) forbidden region beyond a totally internally reflecting interface between two optical mediums. I analyse this situation in my answer here and there is also a great plot of the situation in Ruslan's answer here. Let's think of a 1D barrier ...

0

I'm not quite sure what your goal is. If the user specifies both $p$ and $q$, you end up with one value for the energy, rather than a plot. For a proper plot you'd have to allow for a range of values $p,q\in\mathbb{Z}$. This will of course result in a 3d graph. You may cut that down to 2d, like in the plot you posted, but you'd have to give some relation ...

1

In vacuum (or everywhere else, really), Coulomb's law takes the form $\boldsymbol\nabla \cdot \mathbf{E} = \frac{\rho}{\epsilon}$, whereas in a polarizable material it is convenient to use $\boldsymbol\nabla \cdot \mathbf{D} = \rho_\mathrm{free}$. The $4\pi$ vs $\epsilon$ has more to do with units. As for the sign, can you give a reference?

4

What is the electrical potential difference and why we have to talk about a difference and not about the electrical potential itself? Mathematically, the reason is that the force is proportional the gradient of a (not the) potential function. $$\vec F = -\nabla \phi$$ Note that a potential that differs by an additive constant $$\phi' = \phi + C$$ ...

1

Apparently these interpretations are deduced from equation (1), which doesn't hold in non-extensive systems. So it seems that these potentials are ,inherently, extensive quantities, and have no meaning in non-extensive systems. I do not think that these interpretations depend on (1). They can be derived without (1) or the homogeneous property of ...

0

Correct, your equation (1) does not hold in non-extensive systems. Also, none of the equations hold for a galaxy since it's not in equilibrium. Supposing we do have equilibrium, though, equilibrium statistical mechanics is exactly the tool we need to extend these quantities to non-extensive and microscopic systems. This was one of Gibbs' main goals in his ...

3

(this is a partial answer) One example is the preceding work Barrett, J. W. "The asymmetric monopole and non-newtonian forces." Nature 341.6238 (1989): 131-132. doi:10.1038/341131a0 which is Ref. 13 in the Connes et al. paper. This paper contains one example of asymmetric monopole produced by rotating figure shown about the horizontal axis passing ...

0

In one dimension, motion in a Coulomb-like attracting potential $U=-\frac{\alpha}{|x|}$ is quite ill-defined. I'll now try to explain this for classical particles, then will say some words about quantum mode. Let's consider two cases: 3D motion of a particle nearly free falling into the attracting center, but with nonzero angular momentum $L$. In this ...

0

One way to argue about the so called observations is the sequence of logical implications: Bigger hands$\rightarrow$Bigger bones$\rightarrow$Bigger muscles$\rightarrow$More strength and therefore we can say to some extent say that the people with bigger hands may have an advantage.

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