Talk:Particle in a ring

Untitled
This page owes a lot to the ring_wave_guide page, but I felt like re-writing it to add some more derevation, and the other page is not very clear in places. And the energy is plain wrong :-).

In the comments to the ring wave guide page the energy is given as (n^2 h^2)/(2 m L^2). Note this is h, not hbar, which explains the discrepancy in the equations.


 * Next time you find an article riddled with errors, why not fix them instead of starting another one? 65.29.47.153 11:53, 8 January 2006 (UTC)

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Above undated message substituted from Template:Dashboard.wikiedu.org assignment by PrimeBOT (talk) 06:10, 17 January 2022 (UTC)

merge
Particle in a ring is the same thing as ring wave guide, no? I think "particle in a ring" is the more common phrase. Pfalstad 11:19, 8 January 2006 (UTC)

formula question
It is unclear to me how the second derivative gradient (i.e. d^2/dx^2 + d^2/dy^2) equals (1/r^2)(d^2/dtheta^2) —Preceding unsigned comment added by 76.243.189.248 (talk) 15:37, 5 October 2008 (UTC)

Eigenfunctions
I believe it's ambiguous or misleading to state that $$\psi(\theta)=\frac{1}{\sqrt{2\pi}}e^{\pm i n \theta}$$. This statement implies that $$\psi(\theta)=\frac{1}{\sqrt{2\pi}}e^{-i n \theta} + \frac{1}{\sqrt{2\pi}}e^{+i n \theta}$$. Instead, I think it should be written as $$E_n$$ is written, defining $$n$$ to be positive or negative. I don't want to make this change if I'm mistaken in my understanding, but it does appear to be inconsistent notation. &mdash;Daelin 01:43, 13 December 2008 (UTC)

Is this a stub?
I removed math-stub as this doesn't seem like a stub, and in any case should be a physics one not a maths one. Qetuth (talk) 07:40, 18 December 2011 (UTC)

Check for gauge invariance.
--Ruhtra Patel (talk) 20:28, 10 July 2019 (UTC)An article in AIP Advances suggests that any continuous eigenfunction on a ring will have a wavelength that depends on the arbitrary choice of gauge function: "Nanocircuits in loop structures: Continuous waves preclude gauge invariant wavelengths," has been published online 20 November 2018, in AIP Advances (Vol.8, Issue 11). This article is open access at https://doi.org/10.1063/1.5041020. This implies that continuity should not be imposed on a wave function on a ring or circle. Ruhtra Patel (talk) 19:07, 11 July 2019 (UTC)Since a particle in a ring is not like a particle in a box, the IMPORTANCE of this article ought to be rated higher.