# 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 complex vector formalism of internal harmonic oscillator in zeropoint field, it has been shown by the author that the average energy <[E.
As expected, the collocation of the harmonic oscillator depends on its natural pulsation, while the bandwidth width depends on damping.
It should be noted that, when [alpha] = [beta], Q is unitarily equivalent to a couple of quantum harmonic oscillators, whence the eigenvalues are easily calculated as {[square root of ([[alpha].
We have analyzed the nonlinear dynamics of a harmonic oscillator damped by sliding (or kinetic) friction and have obtained an exact solution.
Hypervirial theorem and parameter differentiation, closed formulation for harmonic oscillator integrals.
ATAKISHIYEV, Construction of the dynamical symmetry group of the relativistic harmonic oscillator by the Infeld-Hull factorization method, Theor.
The exact shape, as it should be, only appears in the case of the harmonic oscillator.
Background appendices are included on mathematical concepts, quantum measurement, the harmonic oscillator, and unitary transformations.
Among specific topics are measuring the irreversible dynamics of a quantum harmonic oscillator, simultaneous wave and particle knowledge in a neutron interferometer, quantum entanglement and partial path information for a double split, quantum-mechanical retrodiction through an extended mean king problem, two cold atoms in a harmonic trap, and experimental polarization state tomography using optimal polarimeters.
Since the early days of modern quantum theory describing the phase of an electromagnetic field mode or harmonic oscillator has been an obstacle to progress.

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