Related papers: Wave Packet under Continuous Measurement via Bohmi…
Spectra of the geometric collective model of atomic nuclei are analyzed to identify chaotic correlations among nonrotational states. The model has been previously shown to exhibit a high degree of variability of regular and chaotic…
The behavior of classical monochromatic waves in stationary media is shown to be ruled by a novel, frequency-dependent function which we call Wave Potential, and which we show to be encoded in the structure of the Helmholtz equation. An…
We develop a dynamical theory, based on a system of ordinary differential equations describing the motion of particles which reproduces the results of quantum mechanics. The system generalizes the Hamilton equations of classical mechanics…
Until recently, wave-particle duality has been thought of as quantum principle without a counterpart in classical physics. This belief was challenged after (i) finding that average dynamics of a classical particle in strong inhomogeneous…
Both classical and wave-mechanical monochromatic waves may be treated in terms of exact ray-trajectories (encoded in the structure itself of Helmholtz-like equations) whose mutual coupling is the one and only cause of any diffraction and…
The non-Hermitian quadratic oscillator studied by Swanson is one of the popular $PT$-symmetric model systems. Here a full classical description of its dynamics is derived using recently developed metriplectic flow equations, which combine…
We investigate the dynamics of a charged particle interacting with a multimode quantized electromagnetic field and obtain an analytic solution for the full electron--field system. This framework enables the calculation of position…
By using a test-function method, we construct $n$ exact solutions of a quantum harmonic oscillator with a time-dependent "spring constant". Any $n$-th solution describes a wave-packet train consisting of $n+1$ packets. Its center oscillates…
The structure of time-dependent Gaussian solutions for the Kostin equation in dissipative quantum mechanics is analyzed. Expanding the generic external potential near the center of mass of the wave packet, one conclude that: the center of…
The broadening of one-dimensional Gaussian wave packets is presented in all textbooks on quantum mechanics. It is used to elucidate Heisenberg's uncertainty relation. The behaviour on a lattice is drastically different if the amplitude…
We introduce a general formalism, based on the stochastic formulation of quantum mechanics, to obtain localized quasi-classical wave packets as dynamically controlled systems, for arbitrary anharmonic potentials. The control is in general…
Effects of noncommutativity are investigated in planar quantum mechanics in the coordinate representation. Generally these issues are addressed by converting to the momentum space. In the first part of the work we show noncommutative…
Statistical measures of chaos have long been used in the study of chaotic dynamics in the framework of the interacting boson model. The use of large number of bosons renders additional studies of chaos possible, that can provide a direct…
The indeterministic character of physical laws is generally considered to be the most important consequence of quantum physics. A deterministic point of view, however, together with the possibility of well defined Hamiltonian trajectories,…
The paper gives a systematic review of the basic ideas of (non-relativistic) quantum mechanics including all changes that result from previous work of the authors. This shows that the new theory is self-consistent and (in certain sense)…
We study the dynamics of the classical and quantum mechanical scattering of a wave packet from an oscillating barrier. Our main focus is on the dependence of the transmission coefficient on the initial energy of the wave packet for a wide…
Bohmian mechanics supplements the quantum wavefunction with deterministic particle trajectories, offering an alternate, dynamical language for quantum theory. However, the Bohmian particle does not affect its guiding wave, so the wave field…
In a recent paper a mathematical model for quantum measurement was presented. The phenomenon of wave particle duality, which is introduced in every beginning course of quantum theory, can be explained using this model. Although it is a…
We analyze relativistic corrections to the wave-packet dynamics of the quantum harmonic oscillator within a perturbative framework. General expressions are derived for the leading-order relativistic contributions to the wave-packet…
Measurement in quantum mechanics is generally described as an irreversible process that perturbs the wavefunction describing a quantum system. In this work we establish a formal connection between the measurement description within the…