We develop a new method of implementing the Hartree-Fock calculations. A class of Gaussian bases is assumed, which includes the Kamimura-Gauss basis-set as well as the set equivalent to the harmonic-oscillator basis-set. By using the Fourier transformation to calculate the interaction matrix elements, we can treat various interactions in a unified manner, including finite-range ones. The presen...

This article presents the parallel implementation of the coupled harmonic oscillator. From the analytical solution of the coupled harmonic oscillator, the design parameters are obtained. After that, a numerical integration of the system with MATLAB, which is used as a tool of benchmark evaluation, is performed. Next, parallel implementation is performed using a well-known approach like OpenMP a...

The aim of this comment is to extend the study of the dynamics of a finite extensibility nonlinear oscillator conducted by Febbo [M. Febbo, A finite extensibility nonlinear oscillator, Applied Mathematics and Computation 217 (2011) 6464-6475]. We show that the linearized harmonic balance method is not sufficiently adequate for this oscillator and that the harmonic balance method without lineari...

We use equations for Faddeev amplitudes to solve the shell-model problem for four nucleons in the model space that includes up to 14h̄Ω harmonic-oscillator excitations above the unperturbed ground state. Twoand three-body effective interactions derived from the Reid93 and Argonne V8’ nucleon-nucleon potentials are used in the calculations. Binding energies, excitations energies, point-nucleon ra...

In the oilfield development stage, more recoverable reserves can be found by using the more sophisticated seismic methods with stimulation. Threecomponent seismic exploration technology comes into being, and it is becoming a major oil exploration seismic technology currently. As the sensitive element of seismic geophone, the performance of the harmonic oscillator is vitally important to the ent...

Everyone who initially studies the harmonic oscillator is immediately barraged with examples of pendula and blocks with springs. If the only significance of the harmonic oscillator lay in these examples it would be pretty limiting. In physics, the harmonic oscillator is an extremely important problem, for a simple reason. Say, for example, you have a potential, V (x), for some system and you wa...

We show that a harmonic oscillator subject to a sudden change of mass produces squeezed states. Our study is based on an approximate analytic solution to the time-dependent harmonic oscillator equation with a subperiod function parameter. This continuous treatment differs from former studies that involve the matching of two time-independent solutions at the discontinuity. This formalism require...

Quantization of a damped harmonic oscillator leads to so called Bateman’s dual system. The corresponding Bateman’s Hamiltonian, being a self-adjoint operator, displays the discrete family of complex eigenvalues. We show that they correspond to the poles of energy eigenvectors and the corresponding resolvent operator when continued to the complex energy plane. Therefore, the corresponding genera...

We study kicked quantum systems by using the squeezed state approach. Taking the kicked quantum harmonic oscillator as an example, we demonstrate that chaos in an underlying classical system can be enhanced as well as suppressed by quantum fluctuations. Three different energy diffusions are observed in the kicked quantum harmonic oscillator, namely, localization, linear diffusion, and quadratic...

The generalized open XXZ model at q root of unity is considered. We review how associated models, such as the q harmonic oscillator, and the lattice sine-Gordon and Liouville models are obtained. Explicit expressions of the local Hamiltonian of the spin 1 2 XXZ spin chain coupled to dynamical degrees of freedom at the one end of the chain are provided. Furthermore, the boundary non-local charge...