Related papers: Classical and Quantum Mechanics via Lie algebras
In 1926, Dirac stated that quantum mechanics can be obtained from classical theory through a change in the only rule. In his view, classical mechanics is formulated through commutative quantities (c-numbers) while quantum mechanics requires…
The concept of number is fundamental to the formulation of any physical theory. We give a heuristic motivation for the reformulation of Quantum Mechanics in terms of non-standard real numbers called Quantum Real Numbers. The standard axioms…
Three problems stand in the way of deriving classical theories from quantum mechanics: those of realist interpretation, of classical properties and of quantum measurement. Recently, we have identified some tacit assumptions that lie at the…
Quantum mechanics is among the most important and successful mathematical model for describing our physical reality. The traditional formulation of quantum mechanics is linear and algebraic. In contrast classical mechanics is a geometrical…
Classical statistical particle mechanics in the configuration space can be represented by a nonlinear Schrodinger equation. Even without assuming the existence of deterministic particle trajectories, the resulting quantum-like statistical…
Where does quantum mechanics part ways with classical mechanics? How does quantum randomness differ fundamentally from classical randomness? We cannot fully explain how the theories differ until we can derive them within a single axiomatic…
A non-classical, non-quantum theory, or NCQ, is any fully consistent theory that differs fundamentally from both the corresponding classical and quantum theories, while exhibiting certain features common to both. Such theories are of…
Sums play a prominent role in the formalisms of quantum mechanics, be it for mixing and superposing states, or for composing state spaces. Surprisingly, a conceptual analysis of quantum measurement seems to suggest that quantum mechanics…
This paper deals with Nancy Cartwright's views on the measurement problem in Quantum Mechanics, as exposed in her book {\it{How the Laws of Physics Lie}}. She does not accept the logic of Quantum Mechanics. It is argued that her proposals,…
The theory of quantum mechanics is examined using non-standard real numbers, called quantum real numbers (qr-numbers), that are constructed from standard Hilbert space entities. Our goal is to resolve some of the paradoxical features of the…
Although classical mechanics and quantum mechanics are separate disciplines, we live in a world where Planck's constant \hbar>0, meaning that the classical and quantum world views must actually {\it coexist}. Traditionally, canonical…
The purpose of this contribution is to give a very brief introduction to Quantum Mechanics for an audience of mathematicians. I will follow Segal's approach to Quantum Mechanics paying special attention to algebraic issues. The usual…
Quantum computing exposes the brilliance of quantum mechanics through computer science and, as such, gives oneself a marvelous and exhilarating journey to go through. This article leads along that journey with a historical and current…
Here I explore a novel no-collapse interpretation of quantum mechanics which combines aspects of two familiar and well-developed alternatives, Bohmian mechanics and the many-worlds interpretation. Despite reproducing the empirical…
After some historical remarks concerning Schroedinger's discovery of wave mechanics, we present a unified formalism for the mathematical description of classical and quantum-mechanical systems, utilizing elements of the theory of operator…
In the thermodynamics of nanoscopic systems the relation between classical and quantum mechanical description is of particular importance. To scrutinize this correspondence we have picked out two 2-dim billiard systems. Both systems are…
Recent advances in our understanding of foundations of quantum mechanics have shown that information can be made objective through quantum states. Such objectification processes, predicted e.g. in a variety of quantum open systems, must…
The dynamical equation of quantum mechanics are rewritten in form of dynamical equations for the measurable, positive marginal distribution of the shifted, rotated and squeezed quadrature introduced in the so called "symplectic tomography".…
We expose the Schr\"odinger quantum mechanics with traditional applications to Hydrogen atom. We discuss carefully the experimental and theoretical background for the introduction of the Schr\"odinger, Pauli and Dirac equations, as well as…
We show that non-relativistic Quantum Mechanics can be faithfully represented in terms of a classical diffusion process endowed with a gauge symmetry of group Z_4. The representation is based on a quantization condition for the realized…