Related papers: On the classical limit of quantum mechanics I
The quantum mechanical formalism for position and momentum of a particle in a one dimensional cyclic lattice is constructively developed. Some mathematical features characteristic of the finite dimensional Hilbert space are compared with…
We derive fundamental limits on measurements of position, arising from quantum mechanics and classical general relativity. First, we show that any primitive probe or target used in an experiment must be larger than the Planck length, $l_P$.…
It is proved here that, as a consequence of the unitary quantum evolution, the expectation value of a properly defined quantum entropy operator (as opposed to the non-evolving von Neumann entropy) can only increase during non adiabatic…
The traditional formulation of the ultimate goal of physics (in the narrower sense of axiomatic theory) involves the derivation of physical laws from first principles. Though, such option doesn't make things easier since the task of the…
The paper gives a systematic review of the basic ideas of (non-relativistic) quantum mechanics including all changes that result from previous work of the authors. This shows that the new theory is self-consistent and (in certain sense)…
We investigate classical-quantum correspondence for kicked Harper model for extremely small values of the Planck constant $\hbar$. In the asymmetric case a pure quantum state shows clear signature of classical diffusive as well as super…
We analyze the problem of one dimensional quantum particle falling in a constant gravitational field, also known as the {\it bouncing ball}, employing a semiclassical approach known as momentous effective quantum mechanics. In this…
Starting from a simple classical framework and employing some stochastic concepts, the basic ingredients of the quantum formalism are recovered. It has been shown that the traditional axiomatic structure of quantum mechanics can be rebuilt,…
How much of the uncertainty in predicting measurement outcomes for non-commuting quantum observables is genuinely quantum mechanical? We provide a natural decomposition of the total entropic uncertainty of two non-commuting observables into…
In this review, we focus on whether a canonical quantization of general relativity can produce testable predictions for cosmology. In particular, we examine how this approach can be used to model the evolution of primordial perturbations.…
By considering (non-relativistic) quantum mechanics as it is done in practice in particular in condensed-matter physics, it is argued that a deterministic, unitary time evolution within a chosen Hilbert space always has a limited scope,…
We show that QM can be represented as a natural projection of a classical statistical model on the phase space $\Omega= H\times H,$ where $H$ is the real Hilbert space. Statistical states are given by Gaussian measures on $\Omega$ having…
The possibility of extending the quantum mechanical superposition principle to free parameters such as the cosmological constant appearing in the Lagrangian of physical theories is examined. If the cosmological constant is subject to a…
We consider a general symplectic transformation (also known as linear canonical transformation) of quantum-mechanical observables in a quantized version of a finite-dimensional system with configuration space isomorphic to $ \mathbb{R}^{q}…
Quantum mechanics marks a radical departure from the classical understanding of Nature, fostering an inherent randomness which forbids a deterministic description; yet the most fundamental departure arises from something different. As shown…
Phenomenological models aiming to join gravity and quantum mechanics often predict effects that are potentially measurable in refined low-energy experiments. For instance, modified commutation relations between position and momentum, that…
Bounds on quantum probabilities and expectation values are derived for experimental setups associated with Bell-type inequalities. In analogy to the classical bounds, the quantum limits are experimentally testable and therefore serve as…
The aim of the paper is to derive essential elements of quantum mechanics from a parametric structure extending that of traditional mathematical statistics. The main extensions, which also can be motivated from an applied statistics point…
A model quantum system is proposed to describe position states of a massive body in flat space on large scales, excluding all standard quantum and gravitational degrees of freedom. The model is based on standard quantum spin commutators,…
In the present contribution we discuss the role of experimental limitations in the classical limit problem. We studied some simple models and found that Quantum Mechanics does not re-produce classical mechanical predictions, unless we…