Related papers: Relating the wave-function collapse with Euler's f…
By defining a prepotential function for the stationary Schr\"odinger equation we derive an inversion formula for the space variable $x$ as a function of the wave-function $\psi$. The resulting equation is a Legendre transform that relates…
Quantum statistical mechanics is formulated as an integral over classical phase space. Some details of the commutation function for averages are discussed, as is the factorization of the symmetrization function used for the grand potential…
The von Neumann collapse of the quantum mechanical wavefunction after a position measurement is derived by a purely probabilistic mechanism in the context of Nelson's stochastic mechanics.
The convenience of coherent state representation is discussed from the viewpoint of what is in a broad sense called the measurement problem in quantum mechanics. Standard quantum theory in coherent state representation is intrinsically…
The relation between continuous functions and random vectors is revealed in the paper that the main meaning is described as, for any given continuous function, there must be a sequence of probability spaces and a sequence of random vectors…
The Bohmian formulation of quantum mechanics is used in order to describe the measurement process in an intuitive way without a reduction postulate in the framework of a deterministic single system theory. Thereby the motion of the hidden…
We analyse a proposition which considers quantum theory as a mere tool for calculating probabilities for sequences of outcomes of observations made by an Observer, who him/herself remains outside the scope of the theory. Predictions are…
We put forward an interpretation of scalar quantum field theory as relativistic quantum mechanics by curing well known problems related to locality. A probabilistic interpretation of quantum field theory similar to quantum mechanics is…
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…
We investigate whether quantum theory can be understood as the continuum limit of a mechanical theory, in which there is a huge, but finite, number of classical 'worlds', and quantum effects arise solely from a universal interaction between…
The additivity of classical probabilities is only the first in a hierarchy of possible sum-rules, each of which implies its successor. The first and most restrictive sum-rule of the hierarchy yields measure-theory in the Kolmogorov sense,…
Throughout quantum mechanics there is statistical balance, in the collective response of an ensemble of systems to differing measurement types. Statistical balance is a core feature of quantum mechanics, underlying quantum mechanical…
In this paper, a modified formulation of generalized probabilistic theories that will always give rise to the structure of Hilbert space of quantum mechanics, in any finite outcome space, is presented and the guidelines to how to extend…
Central to quantum theory, the wavefunction is the complex distribution used to completely describe a quantum system. Despite its fundamental role, it is typically introduced as an abstract element of the theory with no explicit definition.…
We show using a realistic Hamiltonian-type model that definite outcomes of quantum measurements may emerge from quantum evolution of pure states, i.e quantum dynamics provides a deterministic collapse of the wavefunction in a quantum…
We present an alternative formalism of quantum mechanics tailored to statistical ensemble in phase space. The purpose of our work is to show that it is possible to establish an alternative autonomous formalism of quantum mechanics in phase…
The Copenhagen interpretation of quantum mechanics assumes the existence of the classical deterministic Newtonian world. We argue that in fact the Newton determinism in classical world does not hold and in classical mechanics there is…
In this initial paper in a series, we first discuss why classical motions of small particles should be treated statistically. Then we show that any attempted statistical description of any nonrelativistic classical system inevitably yields…
The wave function transformation of the quantum particle considered as a continuous medium was described by the evolution operator with the kernel in the form of path integral. It is shown that this approach allows considering not only…
It is proposed that the paradox of wave-particle duality in quantum mechanics may be resolved using a physical picture analogous to magnetic domains. Within this picture, a quantum particle represents a coherent region of a quantum wave…