Related papers: Probability and complex quantum trajectories
Quantum mechanics does not provide any ready recipe for defining energy density in space, since the energy and coordinate do not commute. To find a well-motivated energy density, we start from a possibly fundamental, relativistic…
We develop a dynamical theory, based on a system of ordinary differential equations describing the motion of particles which reproduces the results of quantum mechanics. The system generalizes the Hamilton equations of classical mechanics…
The position density of a "particle" performing a continuous-time quantum walk on the integer lattice, viewed on length scales inversely proportional to the time t, converges (as t tends to infinity) to a probability distribution that…
The behavior of the probability density function (PDF) transport equation at the limits of the probability space is studied from the point of view of fluid mechanics. Different boundary conditions are considered depending on the nature of…
We study the elusive transition from exponential to post-exponential (algebraic) decay of the probability density of a quantum particle emitted by an exponentially decaying source, in one dimension. The main finding is that the probability…
We follow and modify the Feshbach-Villars formalism by separating the Klein-Gordon equation into two coupled time-dependent Schroedinger equations for particle and antiparticle wave function components with positive probability densities.…
In quantum physics, recent investigations deal with the so-called "quantum trajectory" theory. Heuristic rules are usually used to give rise to "stochastic Schrodinger equations" which are stochastic differential equations of non-usual type…
An extension of the classical action principle obtained in the framework of the gauge transformations, is used to describe the motion of a particle. This extension assigns many, but not all, paths to a particle. Properties of the particle…
We modify the path integral representation of exciton transport in open quantum systems such that an exact description of the quantum fluctuations around the classical evolution of the system is possible. As a consequence, the time…
The propagation of short life time particles with consequently broad mass width are discussed in the context of transport descriptions. In the first part some known properties of finite life time particles such as resonances are reviewed…
In static classical statistical systems the problem of information transport from a boundary to the bulk finds a simple description in terms of wave functions or density matrices. While the transfer matrix formalism is a type of Heisenberg…
Path integrals represent a powerful route to quantization: they calculate probabilities by summing over classical configurations of variables such as fields, assigning each configuration a phase equal to the action of that configuration.…
We solve the time-dependent Schr\"odinger equation by learning the score function, the gradient of the log-probability density, on Bohmian trajectories. In Bohm's formulation of quantum mechanics, particles follow deterministic paths under…
Solutions to the Schr\"{o}dinger equation are examined for a particle inside a cylindrical trap of a circular time-dependent cross-section. Analytical expressions for energy and momentum expectation values are derived with respect to the…
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 predictions of quantum mechanics are probabilistic. Quantum probabilities are extracted using a postulate of the theory called the Born rule, the status of which is central to the "measurement problem" of quantum mechanics. Efforts to…
Despite their theoretical importance, dynamic Bayesian networks associated with quantum processes are currently not accessible experimentally. We here describe a general scheme to determine the multi-time path probability of a Bayesian…
The quantum gravity has great difficulties with application of the probability notion. In given article this problem is analyzed according to algorithmic viewpoint. According to A.N. Kolmogorov, the probability notion can be connected with…
Following our discussion [Physica A, 375 (2007) 123] to associate an analogous probabilistic description with spacetime geometry in the Schwarzschild metric from the macro- to the micro-domain, we argue that there is a possible connection…
We discuss reasons why a probability amplitude, which becomes a probability density after squaring, is considered as one of the most basic ingredients of quantum mechanics. First, the Heisenberg/Schrodinger equation, an equation of motion…