Related papers: An equations-of-motion approach to quantum mechani…
In many situations, one can approximate the behavior of a quantum system, i.e. a wave function subject to a partial differential equation, by effective classical equations which are ordinary differential equations. A general method and…
The problem of quantum harmonic oscillator with "regular+random" square frequency, subjected to "regular+random external force, is considered in framework of representation of the wave function by complex-valued random process. Average…
Dynamical phases are obtained for a quantum thermal engine, whose working medium is a single harmonic oscillator. The dynamics of this engine is obtained by using four steps where in two steps the time dependent frequency is changing. In…
The paper introduces a simple quantum model to calculate in a general way allowed frequencies and energy levels of the anharmonic oscillator. The theoretical basis of the approach has been introduced in two early papers aimed to infer the…
In this paper the relationship between the problem of constructing the ground state energy for the quantum quartic oscillator and the problem of computing mean eigenvalue of large positively definite random hermitean matrices is…
The von Neumann trace form of quantum statistical mechanics is transformed to an integral over classical phase space. Formally exact expressions for the resultant position-momentum commutation function are given. A loop expansion for wave…
Natural frequencies and normal modes are basic properties of a structure which play important roles in analyses of its vibrational characteristics. As their computation reduces to solving eigenvalue problems, it is a natural arena for…
The quantitative contributions of a mixed phase-space to the mean characterizing the distribution of diagonal transition matrix elements and to the variance characterizing the distributions of non-diagonal transition matrix elements are…
In this paper we review a proposed geometrical formulation of quantum mechanics. We argue that this geometrization makes available mathematical methods from classical mechanics to the quantum frame work. We apply this formulation to the…
The use of quantum computing to solve a problem in quantum mechanics is illustrated, step by step, by calculating energies and transition amplitudes in a nonrelativistic quark model. The quantum computations feature the use of variational…
Convenient and simple numerical techniques for performing quantum computations based on matrix representations of Hilbert space operators are presented and illustrated by various examples. The applications include the calculations of…
Quantum phase estimation is at the heart of most quantum algorithms with exponential speedup. In this letter we demonstrate how to utilize it to compute the dynamical response functions of many-body quantum systems. Specifically, we design…
A master equation for the deformed quantum harmonic oscillator interacting with a dissipative environment, in particular with a thermal bath, is derived in the microscopic model by using perturbation theory. The coefficients of the master…
Transitions of many-particle quantum systems between distinct phases at absolute-zero temperature, known as quantum phase transitions, require an exacting treatment of particle correlations. In this work, we present a general…
A combined method for analyzing quantum dynamical equations which uses the Bohmian mechanics and the quantum phase space representation is proposed. It is based on a presentation of the wave function in phase space in a polar form. The…
In this paper, we propose an approach based on the theory of an axiomatic $S$ matrix and partially switching on an interaction, which is extremely suitable for describing the phenomenon of oscillations within the framework of quantum field…
We discuss correspondence between the predictions of quantum theories for rotation angle formulated in infinite and finite dimensional Hilbert spaces, taking as example, the calculation of matrix elements of phase-angular momentum…
This article covers few selected aspects of quantum theory of molecular rotations and vibrations. Triatomic molecules are the simplest systems, which show qualitative characteristics of larger polyatomic molecules. On the minimal example of…
Methods of angular momenta are modified and used to solve some actual problems in quantum mechanics. In particular, we re-derive some known formulas for analytical and numerical calculations of matrix elements of the vector physical…
We introduce the Wigner functional representing a quantum field in terms of the field amplitudes and their conjugate momenta. The equation of motion for the functional of a scalar field point out the relevance of solutions of the classical…