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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 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 COM moves uniformly (i.e., with constant velocity) through space as if it were a point particle with mass equal to the sum M tot of the masses of all the particles. In quantum mechanics a free particle has as state function a plane wave function, which is a non-square-integrable function of well-defined momentum.
The electromagnetic tensor has an electromagnetic four-potential field possessing gauge symmetry. The strong (color) interaction is mediated by gluons, which can have eight color charges. There are eight gluon field strength tensors with corresponding gluon four potentials field, each possessing gauge symmetry.
A parametric oscillator is a harmonic oscillator whose physical properties vary with time. The equation of such an oscillator is + + = This equation is linear in ().By assumption, the parameters and depend only on time and do not depend on the state of the oscillator.
Broken symmetry: The formation of a fermion condensate is often associated with the spontaneous breaking of a symmetry, such as the U(1) gauge symmetry in superconductors. The Bogoliubov transformation provides a way to describe the system in the broken symmetry phase.
The phase diagram is fractal and has structure on all scales. In the figure there is an obvious self-similarity . In the presence of disorder, which is the source of the plateaus seen in the experiments, this diagram is very different and the fractal structure is mostly washed away.
In the semiclassical picture of vibrations (oscillations) of a simple harmonic oscillator, the necessary conditions can occur at the turning points, where the momentum is zero. Classically, the Franck–Condon principle is the approximation that an electronic transition is most likely to occur without changes in the positions of the nuclei in ...