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A simple harmonic oscillator is an oscillator that is neither driven nor damped.It consists of a mass m, which experiences a single force F, which pulls the mass in the direction of the point x = 0 and depends only on the position x of the mass and a constant k.
The one-dimensional harmonic oscillator is readily generalizable to N dimensions, where N = 1, 2, 3, …. In one dimension, the position of the particle was specified by a single coordinate, x. In N dimensions, this is replaced by N position coordinates, which we label x 1, …, x N.
The Fradkin tensor, or Jauch-Hill-Fradkin tensor, named after Josef-Maria Jauch and Edward Lee Hill [1] and David M. Fradkin, [2] is a conservation law used in the treatment of the isotropic multidimensional harmonic oscillator in classical mechanics.
[clarification needed] For each parameter there is a set of ladder operators; these are then a standardized way to navigate one dimension of the root system and root lattice. [2] The ladder operators of the quantum harmonic oscillator or the "number representation" of second quantization are just special cases of this
In two or three dimensions, harmonic oscillators behave similarly to one dimension. The simplest example of this is an isotropic oscillator, where the restoring force is proportional to the displacement from equilibrium with the same restorative constant in all directions.
All of these actually appear in physical problems, the latter ones in the harmonic oscillator, and what is otherwise a bewildering maze of properties of special functions becomes an organized body of facts. For this, see Byron & Fuller (1992, Chapter 5). There occurs also finite-dimensional Hilbert spaces. The space C n is a Hilbert space of ...
The Q factor is a parameter that describes the resonance behavior of an underdamped harmonic oscillator (resonator). Sinusoidally driven resonators having higher Q factors resonate with greater amplitudes (at the resonant frequency) but have a smaller range of frequencies around that frequency for which they resonate; the range of frequencies for which the oscillator resonates is called the ...
Some examples of two-dimensional electron systems achieved experimentally include MOSFET, two-dimensional superlattices of Helium, Neon, Argon, Xenon etc. and surface of liquid Helium. The presence of degenerate energy levels is studied in the cases of Particle in a box and two-dimensional harmonic oscillator , which act as useful mathematical ...