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  Dirac particle confined to a ring

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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 in Open problems by Tavengwa (0 points) [ no revision ]

1 Answer

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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 by Vladimir Kalitvianski (132 points) [ revision history ]
edited Feb 3 by Vladimir Kalitvianski

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