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The quantum-mechanical description of the collective angular motion in a system of two touching fission fragments is proposed. The main peculiarities of excitation spectrum and the structure of the wave functions are investigated. As found,…
Our understanding of quantum field theory rests largely on explicit and controlled calculations in perturbation theory. Because of this, much recent effort has been devoted to improve our grasp of perturbative techniques on cosmological…
We consider a quantum cosmology with a massless background scalar field $\pb$ and adopt a wave packet as the wave function. This wave packet is a superposition of the WKB form wave functions, each of which has a definite momentum of the…
In a two-dimensional approximation, the probability density and current for a photoelectron near the localization of a quantum vortex are theoretically investigated. The wave function in the momentum representation, which we found earlier,…
The properties of the s-wave for a quasi-free particle with position-dependent mass(PDM) have been discussed in details. Differed from the system with constant mass in which the localization of the s-wave for the free quantum particle…
I review arguments demonstrating how the concept of "particle" numbers arises in the form of equidistant energy eigenvalues of coupled harmonic oscillators representing free fields. Their quantum numbers (numbers of nodes of the wave…
In quantum mechanics, the wavefunction predicts probabilities of possible measurement outcomes, but not which individual outcome is realised in each run of an experiment. This suggests that it describes an ensemble of states with different…
The aim of Part II of this paper is to try to describe wave functions on q-deformed versions of position and momentum space. This task is done within the framework developed in Part I of the paper. In order to make Part II self-contained…
The conditions for observation of the particle coordinates, required by logic of the Special Relativity and filtering the quantum field effects, are described. A general relation between the corresponding density of probability and the wave…
Since 1908, when Mie reported analytical expressions for the fields scattered by a spherical particle upon incidence of an electromagnetic plane-wave, generalizing his analysis to the case of an arbitrary incident wave has proved elusive.…
Experiments involving single or few elementary particles are completely described by Quantum Mechanics. Notwithstanding the success of that quantitative description, various aspects of observations, as nonlocality and the statistical…
Total-angular-momentum (TAM) waves provide a set of basis functions for scalar, vector, and tensor fields that can be used in place of plane waves and that reflect the rotational symmetry of the spherical sky. Here we discuss three-point…
We derive the equations of quantum mechanics and quantum thermodynamics from the assumption that a quantum system can be described by an underlying classical system of particles. Each component $\phi_j$ of the wave vector is understood as a…
Physical meaning and a duality of concepts of wave function, action functional, entropy, the Pointing vector, the Einstein tensor and so on can be disclosed by investigating the state of material systems such as thermodynamic and gas…
The hydrogen atom is a system amenable to an exact treatment within Schroedinger's formulation of quantum mechanics according to coordinates in four systems -- spherical polar, paraboloidal, ellipsoidal and spheroconical coordinates; the…
The small amplitude-to-thread ratio helical configuration of a vortex filament in the ideal fluid behaves exactly as de Broglie wave. The complex-valued algebra of quantum mechanics finds a simple mechanical interpretation in terms of…
By introducing concepts of beam shaping into quantum mechanics, we show how interference effects of the quantum wavefunction describing multiple electrons can exactly balance the repulsion among the electrons. With proper shaping of the…
We introduce a quantum phase space representation for the orientation state of extended quantum objects, using the Euler angles and their conjugate momenta as phase space coordinates. It exhibits the same properties as the standard Wigner…
An differential equation for wave functions is proposed, which is equivalent to Schr\"{o}dinger's wave equation and can be used to determine energy-level gaps of quantum systems. Contrary to Schr\"{o}dinger's wave equation, this equation is…
The Wigner distribution function and its spatial-angular moments (intensity-moments) are known as efficient instruments for characterization of complex quasimonochromatic light beams and their transformations. In this paper, the…