Related papers: Probabilistic Parallels in the Classical Limit of …
We describe a scheme for constructing quantum mechanics in which a quantum system is considered as a collection of open classical subsystems. This allows using the formal classical logic and classical probability theory in quantum…
After briefly reviewing the definitions of classical probability densities for position, $P_{CL}(x)$, and for momentum, $P_{CL}(p)$, we present several examples of classical mechanical potential systems, mostly variations on such familiar…
The standard quantum mechanical harmonic oscillator has an exact, dual relationship with a completely classical system: a classical particle running along a circle. Duality here means that there is a one-to-one relation between all…
In finite probability theory, events are subsets of the outcome set. Subsets can be represented by 1-dimensional column vectors. By extending the representation of events to two dimensional matrices, we can introduce "superposition events."…
In quantum physics, the density operator completely describes the state. Instead, in classical physics the mean value of every physical quantity is evaluated by means of a probability distribution. We study the possibility to describe pure…
Real numbers provide a sufficient description of classical physics and all measurable phenomena; however, complex numbers are occasionally utilized as a convenient mathematical tool to aid our calculations. On the other hand, the formalism…
We argue that the quantum probability law follows, in the large N limit, from the compatibility of quantum mechanics with classical-like properties of macroscopic objects. For a finite sample, we find that likely and unlikely measurement…
In this paper we suggest a simple mathematical procedure to derive the classical probability density of quantum systems via Bohr's correspondence principle. Using Fourier expansions for the classical and quantum distributions, we assume…
In the Bayesian approach to probability theory, probability quantifies a degree of belief for a single trial, without any a priori connection to limiting frequencies. In this paper we show that, despite being prescribed by a fundamental…
The density operator of a quantum state can be represented as a complex joint probability of any two observables whose eigenstates have non-zero mutual overlap. Transformations to a new basis set are then expressed in terms of complex…
A new method, dual-space cluster expansion, is proposed to study classical phases transitions in the continuum. It relies on replacing the particle positions as integration variables by the momenta of the relative displacements of particle…
In quantum mechanics, wave functions and density matrices represent our knowledge about a quantum system and give probabilities for the outcomes of measurements. If the combined dynamics and measurements on a system lead to a density matrix…
Quantum particles in a potential are described by classical statistical probabilities. We formulate a basic time evolution law for the probability distribution of classical position and momentum such that all known quantum phenomena follow,…
Both classical and respectively quantum observables can be modeled as somewhat similar examples of random variables. In such a model the associated measurements preserve the values spectrum of an observable but change the corresponding…
In this paper we develop a systematic approach to determine the classical limit of periodic quantum systems and applied it successfully to the problem of the quantum bouncer. It is well known that, for periodic systems, the classical…
The role of probability in quantum mechanics is reviewed, with a discussion of the ``orthodox'' versus the statistical interpretive frameworks, and of a number of related issues. After a brief summary of sources of unease with quantum…
In particle-in-cell simulations and some other statistical computations, the representation of modelled distributions with tracked macro-particles can become locally excessive. Merging or resampling dense clusters or highly-populated phase…
Both the set of quantum states and the set of classical states described by symplectic tomographic probability distributions (tomograms) are studied. It is shown that the sets have common part but there exist tomograms of classical states…
Quantum particles can be obtained from a classical probability distribution in phase space by a suitable coarse graining, whereby simultaneous classical information about position and momentum can be lost. For a suitable time evolution of…
We use the canonical quantization of spherically symetric dust universes, and calculate the expectation value of the quantized metric, $<\Psi|\hat{g}|\Psi>$. Though the classical solutions are singular, and the wave functions have no zero…