We model solar activity cycle as a forced and damped harmonic oscillator consisting of two parts, sinusoidal and transient. The amplitudes, frequencies, phases and decay factors of such a harmonic oscillator are determined by fitting the equation of the sinusoidal and transient parts to the sunspot data for the years 1755–1996 (cycles 1–22) with the results: (i) there is a long-term decreasing ...

The position of the coil in a Kibble balance must be finely controlled. In weighing mode, remains stationary to maintain constant magnetic field. calibration is moved field induce voltage. MSL design based on twin pressure where attached piston one balances. Here we investigate how (and therefore coil) may controlled through careful manipulation gas column under piston. We demonstrate use syrin...

9.1 Harmonic Oscillator 9.1.1 Classical harmonic oscillator and h.o. model 9.1.2 Oscillator Hamiltonian: Position and momentum operators 9.1.3 Position representation 9.1.4 Heisenberg picture 9.1.5 Schrödinger picture 9.2 Uncertainty relationships 9.3 Coherent States 9.3.1 Expansion in terms of number states 9.3.2 Non-Orthogonality 9.3.3 Uncertainty relationships 9.3.4 X-representation 9.4 Phon...

The noncommutative harmonic oscillator in arbitrary dimension is examined. It is shown that the ⋆-genvalue problem can be decomposed into separate harmonic oscillator equations for each dimension. The noncommutative plane is investigated in greater detail. The constraints for rotationally symmetric solutions and the corresponding twodimensional harmonic oscillator are solved. The angular moment...

The Feynman path integral for the generalized harmonic oscillator is reviewed, and it is shown that the path integral can be used to find a complete set of wave functions for the oscillator. Harmonic oscillators with different (time-dependent) parameters can be related through unitary transformations. The existence of generalized coherent states for a simple harmonic oscillator can then be inte...