Related papers: A comment on W. Greiner's "Quantum Mechanics -- An…
We show that the quantum wavefunction, interpreted as the probability density of finding a single non-localized quantum particle, which evolves according to classical laws of motion, is an intermediate description of a material quantum…
This work presents a selective review of results concerning the mathematical interface between the classical and quantum aspects encountered in problems such as the nuclear mean-field dynamics or quantum Brownian motion. It is shown that…
In this paper the Planck function is derived in the frequency domain using the method of oscillators. It is also presented in the wavelength domain and in the wave number domain. The latter is mainly used in spectroscopy for studying…
The Wigner function, which provides a phase-space description of quantum systems, has various applications in quantum mechanics, quantum kinetic theory, quantum optics, radiation transport and others. The concept of Wigner function has been…
The main goal of these lectures -- introduction to Quantum Mechanics for mathematically-minded readers. The second goal is to discuss the mathematical interpretation of the main quantum postulates: transitions between quantum stationary…
Aiming at providing an objective motion picture for the microscopic object described by the wave function, new analysis about motion is presented by use of the point set theory in mathematics, through which we show that a new kind of motion…
We first review the usefulness of the Wigner distribution functions (WDF), associated with Lindblad and pre-master equations, for analyzing a host of problems in Quantum Optics where dissipation plays a major role, an arena where weak…
We introduce kernel estimators for the semicircle law. In this first part of our general theory on the estimators, we prove the consistency and conduct simulation study to show the performance of the estimators. We also point out that…
Irreversible processes of one-dimensional quantum perfect Lorentz gas is studied on the basis of the fundamental laws of physics in terms of the complex spectral analysis associated with the resonance state of the Liouville-von Neumann…
A rigorous microscopic theory for the description of quantum-transport phenomena in systems with open boundaries is proposed. We shall show that the application of the conventional Wigner-function formalism to this problem leads to…
Introductory physics and astronomy courses commonly use Wien's displacement law to explain the colors of blackbodies, including the Sun and other stars, in terms of their temperatures. We argue here that focusing on the peak of the…
A thermodynamic analysis of the harmonic oscillator is presented. Motivation for the study is provided by the blackbody radiation spectrum; when blackbody radiation is regarded as a system of noninteracting harmonic oscillator modes, the…
It is shown that Quantum Mechanics is ambiguous when predicting relative frequencies for an entangled system if the measurements of both subsystems are performed in spatially separated events. This ambiguity gives way to unphysical…
The quantum mechanics description of a physical object stretched in space and stable in time from the relativistic space-time properties point of view, introduced in special theory of relativity, is considered and analysed. The mathematical…
In this article we have developed the formalisms for the modified form of Wien displacement laws for both the gas of electromagnetic waves and a gas of de Broglie waves in Rindler space. In the case of de Broglie waves we assume both…
Interpretations of key concepts, such as uncertainty relations, kinetic energy, value of an observable, probability distributions, the projection or collapse of a wave function postulate, and discrete versus continuous values, that appear…
We present an example revealing that the sign of the "momentum" $P$ of the Wigner "distribution" function $f(q, P)$ is not necessarily associated with the direction of motion in the real world. This aspect, which is not related to the well…
We discuss the argument proposed in Ref.~\cite{Frauchiger-Renner}, and show that it does not particularly illustrate any inconsistency in quantum mechanics, but rather the well known difficulty often described as the \textquotedblleft…
In this comment, we point out some shortcomings in two papers "Fractional quantum mechanics" [Phys. Rev. E 62, 3135 (2000)] and "Fractional Schroedinger equation" [Phys. Rev. E 66, 056108 (2002)]. We prove that the fractional uncertainty…
We treat two possible phenomenological effects of quantum fluctuations of spacetime geometry: spectral line broadening and angular blurring of the image of a distance source. A geometrical construction will be used to express both effects…