# anharmonic oscillator

## Anharmonic oscillator

A generalized version of harmonic oscillator in which the relationship between force and displacement is nonlinear. The harmonic oscillator is a highly idealized system that oscillates with a single frequency, irrespective of the amount of pumping or energy injected into the system. Consequently, the harmonic oscillator's fundamental frequency of vibration is independent of the amplitude of the vibrations. Applications of the harmonic oscillator model abound in various fields, but perhaps the most commonly studied system is the Hooke's law mass-spring system. In the Hooke's law system the restoring force exerted on the mass is proportional to the displacement of the mass from its equilibrium position. This linear relationship between force and displacement mandates that the oscillation frequency of the mass will be independent of the amplitude of the displacement. See Harmonic motion, Harmonic oscillator

In a mechanical anharmonic oscillator, the relationship between force and displacement is not linear but depends upon the amplitude of the displacement. The nonlinearity arises from the fact that the spring is not capable of exerting a restoring force that is proportional to its displacement because of, for example, stretching in the material comprising the spring. As a result of the nonlinearity, the vibration frequency can change, depending upon the system's displacement. These changes in the vibration frequency result in energy being coupled from the fundamental vibration frequency to other frequencies through a process known as parametric coupling. See Vibration

There are many systems throughout the physical world that can be modeled as anharmonic oscillators in addition to the nonlinear mass-spring system. For example, an atom, which consists of a positively charged nucleus surrounded by a negatively charged electronic cloud, experiences a displacement between the center of mass of the nucleus and the electronic cloud when an electric field is present. The amount of that displacement, called the electric dipole moment, is related linearly to the applied field for small fields, but as the magnitude of the field is increased, the field-dipole moment relationship becomes nonlinear, just as in the mechanical system. See Dipole moment

Further examples of anharmonic oscillators include the large-angle pendulum, which exhibits chaotic behavior as a result of its anharmonicity; nonequilibrium semiconductors that possess a large hot carrier population, which exhibit nonlinear behaviors of various types related to the effective mass of the carriers; and ionospheric plasmas, which also exhibit nonlinear behavior based on the anharmonicity of the plasma. In fact, virtually all oscillators become anharmonic when their pump amplitude increases beyond some threshold, and as a result it is necessary to use nonlinear equations of motion to describe their behavior. See Chaos, Pendulum, Semiconductor

McGraw-Hill Concise Encyclopedia of Physics. © 2002 by The McGraw-Hill Companies, Inc.

## anharmonic oscillator

[¦an‚här¦män·ik ′äs·ə‚lād·ər]
(physics)
An oscillating system in which the restoring force opposing a displacement from the position of equilibrium is a nonlinear function of the displacement.
McGraw-Hill Dictionary of Scientific & Technical Terms, 6E, Copyright © 2003 by The McGraw-Hill Companies, Inc.
Mentioned in ?
References in periodicals archive ?
As a second application, we consider the quartic anharmonic oscillator potential that has been a great deal of interest in the analytical and numerical investigations of the one-dimensional anharmonic oscillators because of their importance in molecular vibrations  as well as in solid state physics [35,36] and quantum field theories .
Barakat, "The asymptotic iteration method for the eigenenergies of the anharmonic oscillator potential V(x) = Ax2[alpha] + B[x.sup.2]" Physics Letters A, vol.
Sous, "Solution for the eigenenergies of sextic anharmonic oscillator potential V(x) = [A.sub.6][x.sup.6] + [A.sub.4][x.sup.4] + [A.sub.2][x.sup.2]" Modern Physics Letters A, vol.
Al-Dossary, "The asymptotic iteration method for the eigenenergies of the asymmetrical quantum anharmonic oscillator potentials V(x) = [[summation].sup.2[alpha].sub.j=2]", International Journal of Modern Physics A, vol.
For instance let us show that, at least for certain frequencies, the anharmonic oscillator appears to be a system intrinsically unstable.
In this book, the biquaternion formalism is applied to a good selection of classical textbook quantum systems (e.g., harmonic oscillator, anharmonic oscillator, hydrogen atom, electron spin and orbital angular momentum, and pair-production in QED vacuum).
The Quartic Anharmonic Oscillator. The quartic anharmonic oscillator is another problem in quantum mechanics that has attracted wide interest since Heisenberg studied it in 1925.
Kanwal, "The anharmonic oscillator," Proceedings of the Royal Society A, vol.
High Frequency Anharmonic Oscillator for the Generation of Broadband Deterministic Noise.--U.S.

Site: Follow: Share:
Open / Close