Search results
Results from the WOW.Com Content Network
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 quantum harmonic oscillator; The quantum harmonic oscillator with an applied uniform field [1] The Inverse square root potential [2] The periodic potential The particle in a lattice; The particle in a lattice of finite length [3] The Pöschl–Teller potential; The quantum pendulum; The three-dimensional potentials The rotating system The ...
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.
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.
Though our starting example was the harmonic oscillator, all the math up to this point has been completely general for a particle subject to a conservative force. This formula can be generalized for any one-dimensional physical system by plugging in the corresponding potential energy function.
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 ...