Received 9 September 2007; in final form 20 December 2007 Abstract The fundamental frequencies and the mean values of the internal coordinates are extracted from the trajectories of classical dynamics based on the relation between the classical and the quantum mechanical frequencies using quasi-classical direct ab initio molecular dynamics, where the oscillator amplitude is specified by setting...

The information entropy of Gegenbauer polynomials is relevant since this is related to the angular part of the information entropies of certain quantum mechanical systems such as the harmonic oscillator and the hydrogen atom in D dimensions. We give an effective method to compute the entropy for Gegenbauer polynomials with an integer parameter and obtain the first few terms in the asymptotic ex...

The problem of defining time (or phase) operator for three-dimensional harmonic oscillator has been analyzed. A new formula for this operator has been derived. The results have been used to demonstrate a possibility of representing quantum-mechanical time evolution in the framework of an extended Hilbert space structure. Physical interpretation of the extended structure has been discussed short...

We deal with a generalized statistical description of nonequilibrium complex systems based on least biased distributions given some prior information. A maximum entropy principle is introduced that allows for the determination of the distribution of the fluctuating intensive parameter beta of a superstatistical system, given certain constraints on the complex system under consideration. We appl...

The principle of feedback control is used in a wide variety of physical and engineering problems. For example, it can be applied in a straightforward way to tune the oscillation phase of a harmonic oscillator in order to achieve a desired synchronization. An intriguing and fundamental question is whether continuous feedback can be used to control quantum systems; for instance, if it is possible...

A major problem still confronting molecular simulations is how to determine time-correlation functions of many-body quantum systems. In this paper the results of the maximum entropy ~ME! and singular value decomposition ~SVD! analytic continuation methods for calculating real time quantum dynamics from path integral Monte Carlo calculations of imaginary time time-correlation functions are compa...

This paper is a generalization of previous work on the use of classical canonical transformations to evaluate Hamiltonian path integrals for quantum mechanical systems. Relevant aspects of the Hamiltonian path integral and its measure are discussed and used to show that the quantum mechanical version of the classical transformation does not leave the measure of the path integral invariant, inst...

This paper is a generalization of previous work on the use of classical canonical transformations to evaluate Hamiltonian path integrals for quantum mechanical systems. Relevant aspects of the Hamiltonian path integral and its measure are discussed and used to show that the quantum mechanical version of the classical transformation does not leave the measure of the path integral invariant, inst...

The harmonic oscillator is a very significant problem in quantum mechanics, because it is one of the very few, relatively non-trivial problems that has an exact analytic solution. In addition to this, the harmonic oscillator solution and algebraic formalism has applications throughout modern physics (e.g. many particle systems, QED, quantum field theory, approximations of real systems such as m...