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The resulting differential equation implies that x must oscillate sinusoidally over time, with a period of oscillation that is inherent to the system. x may oscillate with any amplitude, but will always have the same period. Anharmonic oscillators, however, are characterized by the nonlinear dependence of the restorative force on the ...
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.
In the formula above, T is the classical period of either orbit n or orbit m, ... For this reason, Heisenberg investigated the anharmonic oscillator, ...
The equation for describing the period: = shows the period of oscillation is independent of the amplitude, though in practice the amplitude should be small. The above equation is also valid in the case when an additional constant force is being applied on the mass, i.e. the additional constant force cannot change the period of oscillation.
A molecular vibration is a periodic motion of the atoms of a molecule relative to each other, such that the center of mass of the molecule remains unchanged. The typical vibrational frequencies range from less than 10 13 Hz to approximately 10 14 Hz, corresponding to wavenumbers of approximately 300 to 3000 cm −1 and wavelengths of approximately 30 to 3 μm.
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.
The Schrödinger equation for a particle in a spherically-symmetric three-dimensional harmonic oscillator can be solved explicitly by separation of variables. This procedure is analogous to the separation performed in the hydrogen-like atom problem, but with a different spherically symmetric potential V ( r ) = 1 2 μ ω 2 r 2 , {\displaystyle ...
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.