# harmonic oscillator

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Related to harmonic oscillator: Anharmonic oscillator

## Harmonic oscillator

Any physical system that is bound to a position of stable equilibrium by a restoring force or torque proportional to the linear or angular displacement from this position. If such a body is disturbed from its equilibrium position and released, and if damping can be neglected, the resulting vibration will be simple harmonic motion, with no overtones. The frequency of vibration is the natural frequency of the oscillator, determined by its inertia (mass) and the stiffness of its restoring force.

The harmonic oscillator is not restricted to a mechanical system, but might, for example, be electric. Typical electronic oscillators, however, are only approximately harmonic.

If a harmonic oscillator, instead of vibrating freely, is driven by a periodic force, it will vibrate harmonically with the period of the force; initially the natural frequency will also be present, but any damping will eventually remove the natural motion. See Damping, Forced oscillation, Harmonic motion

In both quantum mechanics and classical mechanics, the harmonic oscillator is an important problem. It is one of the few rigorously soluble problems of quantum mechanics. The quantum-mechanical description of electromagnetic, electronic, mesonic, and other fields is usually carried out in terms of a (time) Fourier analysis. The individual Fourier components of noninteracting fields are independent harmonic oscillators. See Anharmonic oscillator

## harmonic oscillator

[här′män·ik ′äs·ə‚lād·ər]
(electronics)
(mechanics)
Any physical system that is bound to a position of stable equilibrium by a restoring force or torque proportional to the linear or angular displacement from this position.
(physics)
Anything which has equations of motion that are the same as the system in the mechanics definition. Also known as linear oscillator; simple oscillator.
References in periodicals archive ?
In the second case, the following differential equation is obtained from (13) for harmonic oscillator as radial part of potential:
In this section we solve the One-Dimensional Nonlinear Schrodinger Equation with Harmonic Oscillator (18) using LADM method by first applying Laplace transform to both sides of the equation (18) as follows:
Huang, "Physical model of multi-scale quantum harmonic oscillator optimization algorithm," Journal of Frontiers of Computer Science and Technology, vol.
Matrix elements over the harmonic oscillator wave function are defined as follows:
As expected, the collocation of the harmonic oscillator depends on its natural pulsation, while the bandwidth width depends on damping.
Therefore, we expect that, for low f, the density matrix for a harmonic oscillator will be given approximately by [7]
In a recent preprint entitled "Spectral analysis of non-commutative harmonic oscillators: The lowest eigenvalue and no crossing (2013)" (arXiv:1304.5578v1), F.
We have analyzed the nonlinear dynamics of a harmonic oscillator damped by sliding (or kinetic) friction and have obtained an exact solution.
Chapter 6 concentrates on harmonic oscillator design and describes an application example.
Although superintegrability and supersymmetric quantum mechanics (SUSYQM) are two separated fields, many quantum systems, such as the harmonic oscillator, the Hydrogen atom, and the Smorodinsky-Winternitz potential, have both supersymmetry and superintegrable conditions [12-16].
He discusses spin, including Lie groups and algebras, and position and momentum in the context of the representation theory of the Heisenberg group, including fundamental concepts from analysis, such as self-adjoint operators of Hilbert space and the Stone-von Neumann Theorem, with application of mathematical theory to physical examples like spin-precession in a magnetic field, the harmonic oscillator, the infinite spherical well, and the hydrogen atom.

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