相关论文: Phase Space Quantum Mechanics - Direct

Space-time is one of the most essential, yet most mysterious concepts in physics. In quantum mechanics it is common to understand time as a marker of instances of evolution and define states around all the space but at one time; while in…

We introduce a numerical method to simulate nonlinear open quantum dynamics of a particle in situations where its state undergoes significant expansion in phase space while generating small quantum features at the phase-space Planck scale.…

In a previous article [H. Bergeron, J. Math. Phys. 42, 3983 (2001)], we presented a method to obtain a continuous transition from classical to quantum mechanics starting from the usual phase space formulation of classical mechanics. This…

We investigate quasi-hermitian quantum mechanics in phase space using standard deformation quantization methods: Groenewold star products and Wigner transforms. We focus on imaginary Liouville theory as a representative example where exact…

The notion of "closed systems" in Quantum Mechanics is discussed. For this purpose, we study two models of a quantum-mechanical system $P$ spatially far separated from the "rest of the universe" $Q$. Under reasonable assumptions on the…

Recent developments in quantum computing suggest that it could be possible to make conditional changes to the state of a quantum mechanical system without resorting to classical observation. It is accomplished through collective response of…

Quantum theory predicts probabilities as well as relative phases between different alternatives of the system. A unified description of both probabilities and phases comes through a generalisation of the notion of a density matrix for…

We present a phase space formulation of quantum mechanics in the Schr\"odinger representation and derive the associated Weyl pseudo-differential calculus. We prove that the resulting theory is unitarily equivalent to the standard…

We present a formulation of quantum mechanics based on orthogonal polynomials. The wavefunction is expanded over a complete set of square integrable basis in configuration space where the expansion coefficients are orthogonal polynomials in…

A version of quantum theory is derived from a set of plausible assumptions related to the following general setting: For a given system there is a set of experiments that can be performed, and for each such experiment an ordinary…

We postulate that physical states are equivalent under coordinate transformations. We then implement this equivalence principle first in the case of one-dimensional stationary systems showing that it leads to the quantum analogue of the…

We examine the problem of defining Lagrangian and Hamiltonian mechanics for a particle moving on a quantum plane $Q_{q,p}$. For Lagrangian mechanics, we first define a tangent quantum plane $TQ_{q,p}$ spanned by noncommuting particle…

In contrast to classical physics, the language of quantum mechanics involves operators and wave functions (or, more generally, density operators). However, in 1932, Wigner formulated quantum mechanics in terms of a distribution function…

We define a p-norm in the context of quantum random variables, measurable operator-valued functions with respect to a positive operator-valued measure. This norm leads to a operator-valued L^p space that is shown to be complete. Various…

It is proposed the scheme of quantum mechanics, in which a Hilbert space and the linear operators are not primary elements of the theory. Instead of it certain variant of the algebraic approach is considered. The elements of noncommutative…

This article outlines a novel interpretation of quantum theory: the Q-based interpretation. The core idea underlying this interpretation, recently suggested for quantum field theories by Drummond and Reid [2020], is to interpret the phase…

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…

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.

We formulate a general method for the study of semiclassical-like dynamics in stable regions of a mixed phase-space, in order to theoretically study the dynamics of quantum accelerator modes. In the simplest case, this involves determining…

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…