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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.
The Hooke's atom is a simple model of the helium atom using the quantum harmonic oscillator. Modelling phonons, as discussed above. A charge q {\displaystyle q} with mass m {\displaystyle m} in a uniform magnetic field B {\displaystyle \mathbf {B} } is an example of a one-dimensional quantum harmonic oscillator: Landau quantization .
The domain of this function is [,] (the ball does not fall through the floor at z = 0), so the distribution is not symmetric as in the case of the simple harmonic oscillator. Again, there is a vertical asymptote at the turning point z = h .
They can also refer specifically to the ladder operators for the quantum harmonic oscillator. In the latter case, the creation operator is interpreted as a raising operator, adding a quantum of energy to the oscillator system (similarly for the lowering operator). They can be used to represent phonons.
The quantum harmonic oscillator (and hence the coherent states) arise in the quantum theory of a wide range of physical systems. [2] For instance, a coherent state describes the oscillating motion of a particle confined in a quadratic potential well (for an early reference, see e.g. Schiff's textbook [3]). The coherent state describes a state ...
Simple harmonic motion can be considered the one-dimensional projection of uniform circular motion. If an object moves with angular speed ω around a circle of radius r centered at the origin of the xy-plane, then its motion along each coordinate is simple harmonic motion with amplitude r and angular frequency ω.
However, many approximate methods work well: Expansion in a Fourier series may provide an equation of motion to arbitrary precision. The term, also called the Duffing term, can be approximated as small and the system treated as a perturbed simple harmonic oscillator. The Frobenius method yields a complex but workable solution.
Figure 2: A simple harmonic oscillator with small periodic damping term given by ¨ + ˙ + =, =, ˙ =; =.The numerical simulation of the original equation (blue solid line) is compared with averaging system (orange dashed line) and the crude averaged system (green dash-dotted line). The left plot displays the solution evolved in time and ...