In this paper, we consider a quantum mechanical system to model the effect of fields on evolution early universe. The consists an inverted oscillator bilinearly coupled set harmonic oscillators. We point out that role noise may be crucial in dynamics oscillator, which is analyzed using theory oscillators with random frequency. Using analogy, argue due fluctuations around its mean value, positiv...

A family of geometric models of quantum relativistic rotating oscillator is defined by using a set of one-parameter deformations of the static (3+1) de Sitter or anti-de Sitter metrics. It is shown that all these models lead to the usual isotropic harmonic oscillator in the non-relativistic limit, even though their relativistic behavior is different. As in the case of the (1+1) models [1], thes...

It is shown that, for a harmonic oscillator in the ground state, Bohmian mechanics and quantum mechanics predict values of opposite sign for certain time correlations.

We evaluate the matrix elements 〈r〉 for the n-dimensional harmonic oscillator in terms of the dual Hahn polynomials and derive a corresponding three-term recurrence relation and a Pasternack-type reflection relation. A short review of similar results for nonrelativistic hydrogen atom is also given. 1. An Introduction The purpose of this note is to present a simple evaluation of the expectation ...

We laser-cool single beryllium ions in a Paul trap to the ground (n = 0) quantum harmonic oscillator state with greater than 90% probability. From this starting point, we can put the atom into various quantum states of motion by application of optical and rf electric fields. Some of these states resemble classical states (the coherent states), while others are intrinsically quantum, such as num...

By factorization of the Hamiltonian describing the quantum mechanics of the continuous q-Hermite polynomial, the creation and annihilation operators of the qoscillator are obtained. They satisfy a q-oscillator algebra as a consequence of the shape-invariance of the Hamiltonian. A second set of q-oscillator is derived from the exact Heisenberg operator solution. Now the q-oscillator stands on th...

We develop a systematic theory of quantum fluctuations in the driven optical parametric oscillator, including the region near threshold. This allows us to treat the limits imposed by nonlinearities to quantum squeezing and noise reduction in this nonequilibrium quantum phase transition. In particular, we compute the squeezing spectrum near threshold and calculate the optimum value. We find that...

We analyze the supersymmetry and the shape invariance of the potentials of the (1+1) relativistic oscillators we have recently proposed [1, 2]. In the general relativity, the geometric models play the role of kinematics, helping us to understand the characteristics of the classical or quantum free motion on a given background. One of the simplest (1+1) geometric models is that of the quantum re...