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The statement that any wavefunction for the particle on a ring can be written as a superposition of energy eigenfunctions is exactly identical to the Fourier theorem about the development of any periodic function in a Fourier series. This simple model can be used to find approximate energy levels of some ring molecules, such as benzene.
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.
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 ...
particle in a box; particle in a ring; particle in a spherically symmetric potential; quantum harmonic oscillator; hydrogen atom; ring wave guide; particle in a one-dimensional lattice (periodic potential) Fock symmetry in theory of hydrogen
The static electric potential can be generated using a set of three electrodes: a ring and two endcaps. In an ideal Penning trap the ring and endcaps are hyperboloids of revolution. For trapping of positive (negative) ions, the endcap electrodes are kept at a positive (negative) potential relative to the ring.
The ring-imaging detection technique was first proposed by Jacques Séguinot and Tom Ypsilantis, working at CERN in 1977. [1] Their research and development, of high precision single-photon detectors and related optics, lay the foundations for the design [2] [3] development [4] and construction of the first large-scale Particle Physics RICH detectors, at CERN's OMEGA facility [5] [6] [7] and ...
Download QR code; Print/export Download as PDF; Printable version; In other projects Wikidata item; ... Particle in a ring; Particle in a spherically symmetric potential;
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).