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An oscillator is a physical system characterized by periodic motion, such as a pendulum, tuning fork, or vibrating diatomic molecule.Mathematically speaking, the essential feature of an oscillator is that for some coordinate x of the system, a force whose magnitude depends on x will push x away from extreme values and back toward some central value x 0, causing x to oscillate between extremes.
The third form of the quartic potential is that of a "perturbed simple harmonic oscillator" or ″pure anharmonic oscillator″ having a purely discrete energy spectrum. The fourth type of possible quartic potential is that of "asymmetric shape" of one of the first two named above.
The Morse potential, named after physicist Philip M. Morse, is a convenient interatomic interaction model for the potential energy of a diatomic molecule.It is a better approximation for the vibrational structure of the molecule than the quantum harmonic oscillator because it explicitly includes the effects of bond breaking, such as the existence of unbound states.
Created Date: 8/30/2012 4:52:52 PM
where is the oscillation amplitude and is a constant defined by the anharmonic coefficients. Second, the shape of the resonance curve is distorted ( foldover effect ). When the amplitude of the (sinusoidal) external force F {\displaystyle F} reaches a critical value F c r i t {\displaystyle F_{\mathrm {crit} }} instabilities appear.
The quantum harmonic oscillator is the quantum-mechanical analog of the classical harmonic oscillator. Because an arbitrary smooth potential can usually be approximated as a harmonic potential at the vicinity of a stable equilibrium point , it is one of the most important model systems in quantum mechanics.
The damping force ensures that the oscillator's response is finite at its resonance frequency. For a time-harmonic driving force which originates from the electric field, Newton's second law can be applied to the electron to obtain the motion of the electron and expressions for the dipole moment, polarization, susceptibility, and dielectric ...
An anharmonic oscillator (in contrast to a simple harmonic oscillator) is one in which the potential energy is not quadratic in the extension q (the generalized position which measures the deviation of the system from equilibrium). Such oscillators provide a complementary point of view on the equipartition theorem.