[en] For the pseudo harmonical oscillator we have built the creation and annihilation operators and the corresponding coherent states. After the deduction of the density operator expression in coherent-state representation in two ways (by then definition and by solving the Bloch equation), we have calculated the expected values of some characteristic physical observables

[en] The delayed response of a damped harmonic oscillator (RLC circuit) to a slow periodic disturbance is presented. This communication is supplementary to the paper published recently (Krupska et al 2001 Eur. J. Phys. 22 133-8)

[en] The occurrence of squeezing effects in couples oscillators, and the transference between them, has been studied in various situations using Hamiltonians involving either nonlinear terms or time-dependent parameters. We consider a simplified scheme generating this effect, and discuss its origin. (author)

[en] In this paper we review the application of the harmonic oscillator quark model to the radiative and the pionic decay widths of the mesons classified according to the harmonic oscillator potential. The algebraic expressions obtained for the decay widths can be used readily to calculate the decay rates of the mesons. The computed decay rates are compared with the experimental values and reasonable agreement between the two is found, especially in the case of the transitions involving the unmixed mesons. (author)

No abstract available

[en] We derive quantum solutions of a generalized inverted or repulsive harmonic oscillator with arbitrary time dependent mass and frequency using the quantum invariant method and linear invariants, and write its wave functions in terms of solutions of a second-order ordinary differential equation that describes the amplitude of the damped classical inverted oscillator. Afterwards, we construct Gaussian wave packet solutions and calculate the fluctuations in coordinate and momentum, the associated uncertainty relation, and the quantum correlations between coordinate and momentum. As a particular case, we apply our general development to the generalized inverted Caldirola-Kanai oscillator. (author)

[en] The classical solution is obtained for the system of two coupled harmonic oscillators with exponentially decaying mass. Using the Feynman path-integral method of quantization an exact propagator for the corresponding quantum system is derived. (author)

[en] In a recent paper we have introduced several possible inequivalent descriptions of the dynamics and of the transition probabilities of a quantum system when its Hamiltonian is not self-adjoint. Our analysis was carried out in finite dimensional Hilbert spaces. This is useful, but quite restrictive since many physically relevant quantum systems live in infinite dimensional Hilbert spaces. In this paper we consider this situation, and we discuss some applications to well known models, introduced in the literature in recent years: the extended harmonic oscillator, the Swanson model and a generalized version of the Landau levels Hamiltonian. Not surprisingly we will find new interesting features not previously found in finite dimensional Hilbert spaces, useful for a deeper comprehension of this kind of physical systems.

[en] This is a review paper concerned with the global consistency of the quantum dynamics of non-commutative systems. Our point of departure is the theory of constrained systems, since it provides a unified description of the classical and quantum dynamics for the models under investigation. We then elaborate on recently reported results concerned with the sufficient conditions for the existence of the Born series and unitarity and turn, afterwards, into analyzing the functional quantization of non-commutative systems. The compatibility between the operator and the functional approaches is established in full generality. The intricacies arising in connection with the explicit computation of path integrals, for the systems under scrutiny, is illustrated by presenting the detailed calculation of the Feynman kernel for the non-commutative two dimensional harmonic oscillator. (author)

[en] We return to the description of the damped harmonic oscillator with an assessment of previous works, in particular the Bateman-Caldirola-Kanai model and a new model proposed by one of the authors. We argue the latter has better high energy behavior and is connected to existing open-systems approaches. - Highlights: → We prove the local equivalence of two damped harmonic oscillator models. → We find different high energy behaviors between the two models. → Based on the local equivalence, we make a simple construction of the coherent states.