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...

Inclusion of the instantaneous Kerr nonlinearity in the FDTD framework leads to implicit equations that have to be solved iteratively. In principle, explicit integration can be achieved with the use of anharmonic oscillator equations, but it tends to be unstable and inappropriate for studying strong-field phenomena like laser filamentation. In this paper, we show that nonlinear susceptibility c...

We show theoretically how a driven harmonic oscillator can be used as a quantum simulator for the non-Markovian damped harmonic oscillator. In the general framework, our results demonstrate the possibility to use a closed system as a simulator for open quantum systems. The quantum simulator is based on sets of controlled drives of the closed harmonic oscillator with appropriately tailored elect...

the potential function of lippincott and schroeder for linear hydrogen bond has been re-examined and extended to nonlinear hydrogen bond. the parameters originally introduced to the potential function by lippincott and schroeder have been determined from the structural parameters such as 0.. .odistance 0-h bond distance, h.. .o distance and hoo angle. thevalidity of harmonic oscillator approxim...

We show that two-dimensional anti-de Sitter spacetime (AdS2) can be put in correspondence, holographically, both with the harmonic oscillator and the free particle. When AdS2 has an horizon the corresponding mechanical system is a thermal harmonic oscillator at temperature given by the Hawking temperature of the horizon. The spectrum of the quantum harmonic oscillator is obtained from classical...