Duffing harmonic oscillator is a common model for nonlinear phenomena in science and engineering. This paper presents He´s Energy Balance Method (EBM) for solving nonlinear differential equations. Two strong nonlinear cases have been studied analytically. Analytical results of the EBM are compared with the solutions obtained by using He´s Frequency Amplitude Formulation (FAF) and numerical solu...

With the help of contraction method we study the harmonic oscillator in spaces with degenerate metrics, namely, on Galilei plane and in the flat 3D Cayley-Klein spaces R 3 (j 2 , j 3). It is shown that the inner degrees of freedom are appeared which physical dimensions are different from the dimension of the space.

The Skyrme-Hartree-Fock-Bogoliubov code HFBTHO using the axial (2D) Transformed Harmonic Oscillator basis is tested against the HFODD (3D Cartesian HO basis) and HFBRAD (radial coordinate) codes. Results of large-scale ground-state calculations are presented for the SLy4 and SkP interactions.

In this paper we will study the 2D-harmonic oscillator in 1:1 resonance. We add a general thirdand fourth order perturbation which is slowly time-dependent, and are interested in the resulting interaction between the unperturbed orbits (states). By treating this system quantummechanically we get a linear system (Schrödinger’s equation) on the infinite dimensional space . We show that this syste...

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...