Related papers: Probability distribution of arrival times in quant…
We show that, in spite of a rather common opinion, quantum mechanics can be represented as an approximation of classical statistical mechanics. The approximation under consideration is based on the ordinary Taylor expansion of physical…
Is quantum mechanics about 'states'? Or is it basically another kind of probability theory? It is argued that the elementary formalism of quantum mechanics operates as a well-justified alternative to 'classical' instantiations of a…
We show that including both the system and the apparatus in the quantum description of the measurement process, and using the concept of conditional probabilities, it is possible to deduce the statistical operator of the system after a…
We revisit the arguments underlying two well-known arrival-time distributions in quantum mechanics, viz., the Aharonov-Bohm and Kijowski (ABK) distribution, applicable for freely moving particles, and the quantum flux (QF) distribution. An…
In this paper we undertake an analysis of the eigenstates of two non self-adjoint operators $\hat q$ and $\hat p$ similar, in a suitable sense, to the self-adjoint position and momentum operators $\hat q_0$ and $\hat p_0$ usually adopted in…
Motivated by a recent prediction [Com. Phys., 6, 195 (2023)] that time-of-flight experiments with ultracold atoms could test different interpretations of quantum mechanics, this work investigates the arrival times predicted by the…
The conceptual setting of quantum mechanics is subject to an ongoing debate from its beginnings until now. The consequences of the apparent differences between quantum statistics and classical statistics range from the philosophical…
This paper is concerned with two questions in the decoherent histories approach to quantum mechanics: the emergence of approximate classical predictability, and the fluctuations about it necessitated by the uncertainty principle. We…
Transition probabilities are an important and useful tool in quantum mechanics. However, in their present form, they are limited in scope and only apply to pure quantum states. In this article we extend their applicability to mixed states…
In the operator formalism of quantum mechanics, the density operator describes the complete statistics of a quantum state in terms of d^2 independent elements, where d is the number of possible outcomes for a precise measurement of an…
We discuss the classical statistics of isolated subsystems. Only a small part of the information contained in the classical probability distribution for the subsystem and its environment is available for the description of the isolated…
In classical physics the joint probability of a number of individually rare independent events is given by the Poisson distribution. It describes, for example, unidirectional transfer of population between the densely and sparsely populated…
Charge transfer statistics of quantum particles is obtained by analysing the time evolution of the many-body wave function. Exploiting properly chosen gauge transformations, we construct the probabilities for transfers of a discrete number…
We discuss how the language of wave functions (state vectors) and associated non-commuting Hermitian operators naturally emerges from classical mechanics by applying the inverse Wigner-Weyl transform to the phase space probability…
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 examine the fundamental aspects of statistical mechanics, dividing the problem into a discussion purely about probability, which we analyse from a Bayesian standpoint. We argue that the existence of a unique maximising probability…
Recent results on the decoherent histories quantization of simple cosmological models (minisuperspace models) are described. The most important issue is the construction, from the wave function, of a probability distribution answering…
It is usually believed that a picture of Quantum Mechanics in terms of true probabilities cannot be given due to the uncertainty relations. Here we discuss a tomographic approach to quantum states that leads to a probability representation…
Given a collection $\{\lambda_1, \dots, \lambda_n\} $ of real numbers, there is a canonical probability distribution on the set of real symmetric or complex Hermitian matrices with eigenvalues $\lambda_1,\ldots,\lambda_n$. In this paper, we…
Probabilistic description of results of measurements and its consequences for understanding quantum mechanics are discussed. It is shown that the basic mathematical structure of quantum mechanics like the probability amplitude, Born rule,…