Related papers: Foundations of Non-linear Quantum Mechanics
Often a non-linear mechanical problem is formulated as a non-linear differential equation. A new method is introduced to find out new solutions of non-linear differential equations if one of the solutions of a given non-linear differential…
Understanding the core content of quantum mechanics requires us to disentangle the hidden logical relationships between the postulates of this theory. Here we show that the mathematical structure of quantum measurements, the formula for…
This paper deals with the foundations of quantum mechanics. We start by outlining the characterisation, due to Birkhoff and Von Neumann, of the logical structures of the theories of classical physics and quantum mechanics, as boolean and…
We consider the situation of a physical entity that is the compound entity consisting of two 'separated' quantum entities. In earlier work it has been proven by one of the authors that such a physical entity cannot be described by standard…
On the base of years of experience of working on the problem of the physical foundation of quantum mechanics the author offers principles of solving it. Under certain pressure of mathematical formalism there has raised a hypothesis of…
The variational principle serves as a fundamental framework for describing equilibrium states of physical systems via the minimization or extremization of an energy-like functional. While quantum algorithms have demonstrated promising…
Four formulations of quantum mechanics on noncommutative Moyal phase spaces are reviewed. These are the canonical, path-integral, Weyl-Wigner and systematic formulations. Although all these formulations represent quantum mechanics on a…
The purpose of this paper is to present an introduction to a point of view for discrete foundations of physics. In taking a discrete stance, we find that the initial expression of physical theory must occur in a context of noncommutative…
We recently introduced a particular nonlinear generalization of quantum mechanics which has the property that it is exactly solvable in terms of the eigenvalues and eigenfunctions of the Hamiltonian of the usual linear quantum mechanics…
The foundations of statistical mechanics, namely how equilibrium hypothesis emerges microscopically from quantum theory, is explored through investigating the environment-induced quantum decoherence processes. Based on the recent results on…
The stochastic theory of non-relativistic quantum mechanics presented here relies heavily upon the theory of stochastic processes, with its definitions, theorems and specific vocabulary as well. Its main hypothesis states indeed that the…
A general non-commutative quantum mechanical system in a central potential $V=V(r)$ in two dimensions is considered. The spectrum is bounded from below and for large values of the anticommutative parameter $\theta $, we find an explicit…
We reconsider the generalization of standard quantum mechanics in which the position operators do not commute. We argue that the standard formalism found in the literature leads to theories that do not share the symmetries present in the…
A large spectrum of problems in classical physics and engineering, such as turbulence, is governed by nonlinear differential equations, which typically require high-performance computing to be solved. Over the past decade, however, the…
The aim of this paper is to analyze the reconstructability of quantum mechanics from classical conditional probabilities representing measurement outcomes conditioned on measurement choices. We will investigate how the quantum mechanical…
The present paper is based upon equations obtained in an earlier paper by the author devoted to a new formulation of quantum electrodynamics. The equations describe the structure of the electron as well as its motion in external fields,…
Quantization of the nonlinear supersymmetry faces a problem of a quantum anomaly. For some classes of superpotentials, the integrals of motion admit the corrections guaranteeing the preservation of the nonlinear supersymmetry at the quantum…
A qualitative but formalized representation of microstates is first established quite independently of the quantum mechanical mathematical formalism, exclusively under epistemological-operational-methodological constraints. Then, using this…
The physical constructs underlying the properties of quantum mechanics are explored. Arguments are given that the particle wave function as well as photon and phonon quanta must derive from a more fundamental physical construct that has not…
Non-relativistic quantum mechanics is reformulated here based on the idea that relational properties among quantum systems, instead of the independent properties of a quantum system, are the most fundamental elements to construct quantum…