Related papers: On the classical limit of quantum mechanics I
The quantum mechanical commutation relations, which are directly related to the Heisenberg uncertainty principle, have a crucial importance for understanding the quantum mechanics of students. During undergraduate level courses, the…
Quantum mechanics rests on the assumption that time is a classical variable. As such, classical time is assumed to be measurable with infinite accuracy. However, all real clocks are subject to quantum fluctuations, which leads to the…
We introduce a simple deformed quantization prescription that interpolates the classical and quantum sectors of Weinberg's nonlinear quantum theory. The result is a novel classical limit where $\hbar$ is kept fixed while a dimensionless…
This work concerns a study of the quantum mechanical extension of the work of Horwitz et al. [1] on the stability of classical Hamiltonian systems by geometrical methods. Simulations are carried out for several important examples, these…
Although Planck's constant h is currently regarded as the elementary quantum of action appearing in quantum theory, it can also be interpreted as the multiplicative scale factor setting the scale of classical zero-point radiation appearing…
For classical field theories with probabilistic initial conditions the classical field observables are an idealization. Their arbitrarily precise values poorly reflect the characteristic uncertainty in the presence of substantial…
In a previous paper a formalism to analyze the dynamical evolution of classical and quantum probability distributions in terms of their moments was presented. Here the application of this formalism to the system of a particle moving on a…
The notion of incompressible momentum observables is introduced. It is shown that when the metric in a manifold has a certain form, a set of canonically conjugate variables Xk and Pk in which Pk are incompressible, can be constructed. Based…
Uncertainty relations provide fundamental limits on what can be said about the properties of quantum systems. For a quantum particle, the commutation relation of position and momentum observables entails Heisenberg's uncertainty relation. A…
The classical limit of quantum mechanics is investigated, by focusing on the study of the center of mass of a many-body system where each particle is described by quantum mechanics. We study how, in the limit when the number of particles…
A geometric construction of the arrival time in conventional quantum mechanics is presented. It is based on a careful mathematical analysis of different quantization procedures for classical observables as functions of positions and…
There exists a paradigm in which Quantum Mechanics is an exclusively developed theory to explain phenomena on a microscopic scale. As the Planck's constant is extremely small, $h\sim10^{-34}{J.s}$, and as in the relation of de Broglie the…
Two generalizations of Kempf's quadratic canonical commutation relation in one dimension are considered. The first one is the most general quadratic commutation relation. The corresponding nonzero minimal uncertainties in position and…
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…
We construct an operational formulation of classical mechanics without presupposing previous results from analytical mechanics. In doing so, several concepts from analytical mechanics will be rediscovered from an entirely new perspective.…
Since their discovery in 1927, the Heisenberg Inequalities have become an icon of quantum mechanics. Often inappropriately referred to as the Uncertainty Principle, these inequalities relating the standard deviations of the position and…
We use non-standard analysis to define a category $^\star\!\operatorname{Hilb}$ suitable for categorical quantum mechanics in arbitrary separable Hilbert spaces, and we show that standard bounded operators can be suitably embedded in it. We…
Classical transport equations with probabilistic initial conditions can be viewed as quantum systems. In a discrete version they are probabilistic automata. The time-local probabilistic information is encoded in a classical wave function.…
In our previous papers we were interested in making a reconstruction of quantum mechanics according to classical mechanics. In this paper we suspend this program for a while and turn our attention to a theme in the frontier of quantum…
It is generally believed that classical regime emerges as a limiting case of quantum theory. Exploring such quantum-classical correspondences in a more transparent manner is central to the deeper understanding of foundational aspects and…