• Register
PhysicsOverflow is a next-generation academic platform for physicists and astronomers, including a community peer review system and a postgraduate-level discussion forum analogous to MathOverflow.

Welcome to PhysicsOverflow! PhysicsOverflow is an open platform for community peer review and graduate-level Physics discussion.

Please help promote PhysicsOverflow ads elsewhere if you like it.


New printer friendly PO pages!

Migration to Bielefeld University was successful!

Please vote for this year's PhysicsOverflow ads!

Please do help out in categorising submissions. Submit a paper to PhysicsOverflow!

... see more

Tools for paper authors

Submit paper
Claim Paper Authorship

Tools for SE users

Search User
Reclaim SE Account
Request Account Merger
Nativise imported posts
Claim post (deleted users)
Import SE post

Users whose questions have been imported from Physics Stack Exchange, Theoretical Physics Stack Exchange, or any other Stack Exchange site are kindly requested to reclaim their account and not to register as a new user.

Public \(\beta\) tools

Report a bug with a feature
Request a new functionality
404 page design
Send feedback


(propose a free ad)

Site Statistics

198 submissions , 156 unreviewed
4,894 questions , 2,072 unanswered
5,309 answers , 22,537 comments
1,470 users with positive rep
801 active unimported users
More ...

  Dirac particle confined to a ring

+ 0 like - 0 dislike
Is it possible to have a relativistic fermion of charge -q, confined to a ring around a relatively heavy particle of charge +q, such that the
fermion forms standing waves with n, nodes along the ring. If
possible, would the system be stable and where can I find the Dirpossible, would the system be stable and where can I find the Dirac
solution for that system.
asked Jan 30, 2020 in Open problems by Tavengwa (0 points) [ no revision ]

1 Answer

+ 0 like - 0 dislike

To some extent, yes, it is possible: you take a heavy nucleus with $+q$ and attach one electron to it. It will be an ion with the total charge $+q-1$ and with Hydrogen-like orbital motions, except for being more relativistic and with the ground state still spherically symmetric. All the other configurations ("ring-like") are quasi-stable due to possibility to emit photons with getting into the "atomic" ground state. Read something about Hydrogen-like ions.

P.S. In principle, one can imagine a superposition of different states with different quantum numbers such that the wave packet will ressemble more or less localized  "particle" moving around the nucleus (kind of a "coherent state"). But again, such state is only quasi-stationary since there is still interaction with photon field leading to decay such an atomic (ionic) state into another superposition with smaller atomic energies and with several photons flying away.

answered Jan 31, 2020 by Vladimir Kalitvianski (92 points) [ revision history ]
edited Feb 3, 2020 by Vladimir Kalitvianski

Your answer

Please use answers only to (at least partly) answer questions. To comment, discuss, or ask for clarification, leave a comment instead.
To mask links under text, please type your text, highlight it, and click the "link" button. You can then enter your link URL.
Please consult the FAQ for as to how to format your post.
This is the answer box; if you want to write a comment instead, please use the 'add comment' button.
Live preview (may slow down editor)   Preview
Your name to display (optional):
Privacy: Your email address will only be used for sending these notifications.
Anti-spam verification:
If you are a human please identify the position of the character covered by the symbol $\varnothing$ in the following word:
Then drag the red bullet below over the corresponding character of our banner. When you drop it there, the bullet changes to green (on slow internet connections after a few seconds).
To avoid this verification in future, please log in or register.

user contributions licensed under cc by-sa 3.0 with attribution required

Your rights