Related papers: Foundations of Non-linear Quantum Mechanics
Quantum mechanics---the theory describing the fundamental workings of nature---is famously counterintuitive: it predicts that a particle can be in two places at the same time, and that two remote particles can be inextricably and…
A quantum mechanical model for the systems consisting of interacting bodies is considered. The model takes into account the noncommutativity of the space and impulse operators and the correlation equations for the indeterminacy of these…
Three basic postulates for Quantum Theory are proposed, namely the Probability, Maximum-Speed and Hilbert-Space postulates. Subsequently we show how these postulates give rise to well-known and widely used quantum results, as the…
It is usually stated that quantum mechanics presents problems with the identity of particles, the most radical position -supported by E. Schrodinger- asserting that elementary particles are not individuals. But the subject goes deeper, and…
Quantum-mechanical wave equation for a particle with spin 1 is investigated in presence of external magnetic field in spaces with non-Euclidean geometry with constant positive curvature. Separation of the variable is performed; differential…
In this paper we derive structure theorems that characterize the spaces of linear and non-linear differential operators that preserve finite dimensional subspaces generated by polynomials in one or several variables. By means of the useful…
Operational frameworks are very useful to study the foundations of quantum mechanics, and are sometimes used to promote antirealist attitudes towards the theory. The aim of this paper is to review three arguments aiming at defending an…
The objective of this series of three papers is to axiomatically derive quantum mechanics from classical mechanics and two other basic axioms. In this first paper, Schreodinger's equation for the density matrix is fist obtained and from it…
I propose a new and direct connection between classical mechanics and quantum mechanics where I derive the quantum mechanical propagator from a variational principle. This variational principle is Hamilton's modified principle generalized…
The spread of the wave-function, or quantum uncertainty, is a key notion in quantum mechanics. At leading order, it is characterized by the quadratic moments of the position and momentum operators. These evolve and fluctuate independently…
We propose a new form of nonrelativistic quantum mechanics which is based on a quantum version of the action principle.
In mathematical aspect, we introduce quantum algorithm and the mathematical structure of quantum computer. Quantum algorithm is expressed by linear algebra on a finite dimensional complex inner product space. The mathematical formulations…
The mathematical formulation of Quantum Mechanics is derived from purely operational axioms based on a general definition of "experiment" as a set of transformations. The main ingredient of the mathematical construction is the postulated…
Within the framework of the algebraic approach the problem of hidden parameters in quantum mechanics is surveyed. It is shown that the algebraic formulation of quantum mechanics permits introduction of a specific hidden parameter, which has…
This paper considers a generalization of the notion of quantum observables in ontological models of quantum mechanics. Within this framework it is possible to construct physical models where quantum noncommutativity can arise dynamically.…
General features of nonlinear quantum mechanics are discussed in the context of applications to two-level atoms.
We consider classical and quantum mechanics related to an additional noncommutativity, symmetric in position and momentum coordinates. We show that such mechanical system can be transformed to the corresponding one which allows employment…
Some of the problems connected with the interpretation of quantum mechanics are enumerated, in particular those related to some well known paradoxes and, above all, to the measurement process. We then show how the so called "Physics…
The following two papers form a natural development of a previous series of three articles on the foundations of quantum mechanics; they are intended to take the theory there developed to its utmost logical and epistemological consequences.…
Linear oscillators contribute to most branches of contemporary quantum science. They have already successfully served as quantum sensors and memories, found applications in quantum communication, and hold promise for cluster-state-based…