Related papers: Foundations of Non-linear Quantum Mechanics
Biconformal spaces contain the essential elements of quantum mechanics, making the independent imposition of quantization unnecessary. Based on three postulates characterizing motion and measurement in biconformal geometry, we derive…
General non-commutative supersymmetric quantum mechanics models in two and three dimensions are constructed and some two and three dimensional examples are explicitly studied. The structure of the theory studied suggest other possible…
After the development of a self-consistent quantum formalism nearly a century ago, there ensued a quest to understand the often counterintuitive predictions of the theory. These endeavors invariably begin with the assumption of the "truth"…
To enhance the consistency between the quantum descriptions of waves and particles, we quantise mechanical point particles in this paper in the same physically-motivated way as we previously quantised light in quantum electrodynamics…
The role of operational quantum mechanics, quantum axiomatics and quantum structures in general is presented as a contribution to a compendium on quantum physics, its history and philosophy.
The non-individuals interpretation of quantum mechanics is presented with the aim of clarifying it and highflying some of its salient features. Alternative formulations of it are proposed and examined.
An extension of the Liouville-von Neumann dynamics to a Nambu-type dynamics is proposed. The resulting theory is the first version of nonlinear QM which is free from internal inconsistencies.
Quantum mechanics, the fundamental theory that governs the behaviour of matter and energy at microscopic scales, forms the foundation of quantum computing and quantum information science. As quantum technologies progress, software engineers…
We derive noncommutative multi-particle quantum mechanics from noncommutative quantum field theory in the nonrelativistic limit. Paricles of opposite charges are found to have opposite noncommutativity. As a result, there is no…
Relativistic quantum mechanics can be considered to have begun with a search for wave equations corresponding to each intrinsic spin. However, relativistic quantum physics differs fundamentally from the non-relativistic wave mechanics. It…
Is quantum mechanics about 'states'? Or is it basically another kind of probability theory? It is argued that the elementary formalism of quantum mechanics operates as a well-justified alternative to 'classical' instantiations of a…
Nonreflexive quantum mechanics is a formulation of quantum theory based on a non-classical logic termed \ita{nonreflexive logic} (a.k.a. `non-reflexive'). In these logics, the standard notion of identity, as encapsulated in classical logic…
Starting with the first-order singular Lagrangian containing the redundant variables, the noncommutative quantum mechanics on a curved space is investigated by the constraint star-product quantization formalism of the projection operator…
We investigate the generation of nonlinear operators with single photon sources, linear optical elements and appropriate measurements of auxiliary modes. We provide a framework for the construction of useful single-mode and two-mode quantum…
This paper is devoted to the construction and analysis of the Wigner functions for noncommutative quantum mechanics, their marginal distributions and star-products, following a technique developed earlier, {\it viz\/,} using the unitary…
The response of a test particle, both for the free case and under the harmonic oscillator potential, to circularly polarized gravitational waves is investigated in a noncommutative quantum mechanical setting. The system is quantized…
A non-relativistic quantum mechanical theory is proposed that describes the universe as a continuum of worlds whose mutual interference gives rise to quantum phenomena. A logical framework is introduced to properly deal with propositions…
Since the beginning, quantum mechanics has raised major foundational and interpretative problems. Foundational research has been an important factor in the development of quantum cryptography, quantum information theory and, perhaps one…
We discuss the uncertainty relations in quantum mechanics on noncommutative plane. In particular, we show that, for a given state at most one out of three basic nontrivial uncertainty relations can be saturated. We consider also in some…
We consider the quantum mechanics of a particle on a noncommutative two-sphere with the coordinates obeying an SU(2)-algebra. The momentum operator can be constructed in terms of an $SU(2)\times SU(2)$-extension and the Heisenberg algebra…