single-valence electron atoms are an important class of atoms. their oscillator strengths are their important properties. knowing the oscillator strengths one can easity calculate the transition probabilities of the spectral lines and hence the lifetimes of energy levels of most atoms. the oscillator strengths of the spectral lines of most atoms are not knoen with sufficient accuracy due to the...

Adelic quantum mechanics is formulated. The corresponding model of the harmonic oscillator is considered. The adelic harmonic oscillator exhibits many interesting features. One of them is a softening of the uncertainty relation.

A "Schrodinger cat"-like state of matter was generated at the single atom level. A trapped 9Be+ ion was laser-cooled to the zero-point energy and then prepared in a superposition of spatially separated coherent harmonic oscillator states. This state was created by application of a sequence of laser pulses, which entangles internal (electronic) and external (motional) states of the ion. The Schr...

In this paper we derive an exact master equation for two coupled quantum harmonic oscillators interacting via bilinear coupling with a common environment at arbitrary temperature made up of many harmonic oscillators with a general spectral density function. We first show a simple derivation based on the observation that the two harmonic oscillator model can be effectively mapped into that of a ...

A new technique for evaluating the absolute free energy of large molecules is presented. Quantum-mechanical contributions to the intramolecular torsions are included via the torsional path integral Monte Carlo ~TPIMC! technique. Importance sampling schemes based on uncoupled free rotors and harmonic oscillators facilitate the use of the TPIMC technique for the direct evaluation of quantum parti...

We show that the nonlinear auxiliary equation for the invariant introduced by Lewis and Riesenfeld for a time-dependent harmonic oscillator is satisfied by the amplitude of a complex soltuion to the classical equation of motion. One-parameter squeezed Gaussian states are found whose parameter denotes the mixing of positive and negative frequency solutions. The minimization of the energy expecta...

Completely integrable Hamiltonians defining classical mechanical systems of N coupled oscillators are obtained from Poisson realizations of Heisenberg–Weyl, harmonic oscillator and sl(2, IR) coalgebras. Various completely integrable deformations of such systems are constructed by considering quantum deformations of these algebras. Explicit expressions for all the deformed Hamiltonians and const...

This article deals with a quantum-mechanical system which generalizes the ordinary isotropic harmonic oscillator system. We give the coefficients connecting the polar and Cartesian bases for D = 2 and the coefficients connecting the Cartesian and cylindrical bases as well as the cylindrical and spherical bases for D = 3. These interbasis expansion coefficients are found to be analytic continuat...

In the framework of the Lindblad theory for open quantum systems the damping of the harmonic oscillator is studied. A generalization of the fundamental constraints on quantum mechanical diffusion coefficients which appear in the master equation for the damped quantum oscillator is presented; the Schrödinger and Heisenberg representations of the Lindblad equation are given explicitly. On the bas...