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In quantum mechanics, the case of a particle in a one-dimensional ring is similar to the particle in a box. The Schrödinger equation for a free particle which is restricted to a ring (technically, whose configuration space is the circle S 1 {\displaystyle S^{1}} ) is
If a particle is confined to the motion of an entire ring ranging from 0 to , the particle is subject only to a periodic boundary condition (see particle in a ring). If a particle is confined to the motion of − π 2 {\textstyle -{\frac {\pi }{2}}} to π 2 {\textstyle {\frac {\pi }{2}}} , the issue of even and odd parity becomes important.
A storage ring is a type of circular particle accelerator in which a continuous or pulsed particle beam may be kept circulating, typically for many hours. Storage of a particular particle depends upon the mass , momentum , and usually the charge of the particle to be stored.
On 4 July 2012, the discovery of a new particle with a mass between 125 and 127 GeV/c 2 was announced; physicists suspected that it was the Higgs boson. Since then, the particle has been shown to behave, interact, and decay in many of the ways predicted for Higgs particles by the Standard Model, as well as having even parity and zero spin, two ...
Some trajectories of a particle in a box according to Newton's laws of classical mechanics (A), and according to the Schrödinger equation of quantum mechanics (B–F). In (B–F), the horizontal axis is position, and the vertical axis is the real part (blue) and imaginary part (red) of the wave function.
The geometry allows for a very uniform magnetic field to be established in the ring. Muon g − 2 (pronounced "gee minus two") is a particle physics experiment at Fermilab to measure the anomalous magnetic dipole moment of a muon to a precision of 0.14 ppm, [1] which is a sensitive test of the Standard Model. [2]
A free particle with mass in non-relativistic quantum mechanics is described by the free Schrödinger equation: (,) = (,) where ψ is the wavefunction of the particle at position r and time t . The solution for a particle with momentum p or wave vector k , at angular frequency ω or energy E , is given by a complex plane wave :
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).