Related papers: de Broglie's Exact Trajectories
A new, very different physical model of the universe is proposed. Its virtues include unifying relativity and quantum mechanics, and particles with de Broglie waves. It also appears to provide a truly unified physical basis for…
In this paper we study the dynamics of trajectory of a spinning particle in a Schwarzschild spacetime involving a global monopole. We set up the equations of motion and find three types of trajectories. We study the conditions that a…
The behavior of spinning particles in the stationary homogeneous electric field is considered and trajectories are found for various spin orientations. We study the acceleration of spinning particles by an electric field, as well as the…
In quantum mechanics, the time evolution of particles is given by the Schr\"odinger equation. It is valid in a nonrelativistic regime where the interactions with the particle can be modelled by a potential and quantised fields are not…
We investigate the tachyonic nature of the de Broglie matter waves associated with a free quantum object to show that granting reality to them would lend completeness to the quantum description of reality. Basing on the robustness of the…
The Brownian motion of a test particle interacting with a quantum scalar field in the presence of a perfectly reflecting boundary is studied in (1 + 1)-dimensional flat spacetime. Particularly, the expressions for dispersions in velocity…
In 1952 Bohm presented a theory about non-relativistic point-particles moving along deterministic trajectories and showed how it reproduces the predictions of standard quantum theory. This theory was actually presented before by de Broglie…
We consider the nonlinear Schr\"odinger equation with nonzero conditions at infinity in $\R^2$. We investigate the existence of traveling waves that are periodic in the direction transverse to the direction of propagation and minimize the…
Here I present a new discrete model of quantum mechanics for relativistic 1-electron systems, in which particle movement is described by a directed space-time graph with attached 4-spinors, but without any continuous wave functions. These…
The de Broglie-Bohm interpretation of quantum mechanics aims to give a realist description of quantum phenomena in terms of the motion of point-like particles following well-defined trajectories. This work is concerned by the de…
In this paper we propose an ab initio method to solve quantum many-body problems of molecular dynamics where both the electronic and the nuclear degrees are represented by ensembles of trajectories and guiding waves in physical space. Both…
In this paper we focus our attention on a particle that follows a unidirectional quantum walk, an alternative version of the nowadays widespread discrete-time quantum walk on a line. Here the walker at each time step can either remain in…
Quantum trajectories, originating from the de Broglie-Bohm (dBB) hydrodynamic description of quantum mechanics, are used to construct time-correlation functions in an initial value representation (IVR). The formulation is fully quantum…
An embedding method for solving the time-dependent Schr\"odinger equation is developed using the Dirac-Frenkel variational principle. Embedding allows the time-evolution of the wavefunction to be calculated explicitly in a limited region of…
The Klein-Gordon equation is a useful test arena for quantum cosmological models described by the Wheeler-DeWitt equation. We use the decoherent histories approach to quantum theory to obtain the probability that a free relativistic…
Admitting the validity of Lorentz transformations for the space as time coordinates of the same event we derive their differential form in order to underline the correct prerequisites for the application of time and length contraction or…
In the present paper we consider the semiclassical magnetic Schr\"odinger equation, which describes the dynamics of particles under the influence of a magnetic field. The solution of the time-dependent Schr\"odinger equation is approximated…
We present Lagrangian which implies both necessary constraints and dynamical equations for position and spin of relativistic spin one-half particle. The model is consistent for any value of magnetic moment $\mu$ and for arbitrary…
The transient picture for a Bloch electron accelerating in an arbitrarily time-dependent homogeneous electric field is developed. The temporal sequence for the analysis includes the instant after electron injection, followed by the time…
We use the time-dependent invariant method in a geometric approach (Jacobi fields) to quantize the motion of a free falling point particle in the Schwarzschild black hole. Assuming that the particle comes from infinity, we obtain the…