Related papers: Classical trajectories compatible with quantum mec…
The quantum trajectories in the de Broglie-Bohm formulation of quantum mechanics depend on an additional quantum potential derived from the full wave solution of Schr\"odinger's equation. The task of supplying collectively all the correct…
With an apparent delay of over one century with respect to the development of standard Analytical Mechanics, but still in fully classical terms, the behavior of classical monochromatic wave beams in stationary media is shown to be ruled by…
This paper examines the complex trajectories of a classical particle in the potential V(x)=-cos(x). Almost all the trajectories describe a particle that hops from one well to another in an erratic fashion. However, it is shown analytically…
The relationship between classical and quantum mechanics is explored in an intuitive manner by the exercise of constructing a wave in association with a classical particle. Using special relativity, the time coordinate in the frame of…
Classical transport equations with probabilistic initial conditions can be viewed as quantum systems. In a discrete version they are probabilistic automata. The time-local probabilistic information is encoded in a classical wave function.…
The behavior of classical and quantum wave beams in stationary media is shown to be ruled by a "Wave Potential" function encoded in Helmholtz-like equations, determined by the structure itself of the beam and taking, in the quantum case,…
Classical statistical particle mechanics in the configuration space can be represented by a nonlinear Schrodinger equation. Even without assuming the existence of deterministic particle trajectories, the resulting quantum-like statistical…
The usual Heisenberg uncertainty relation for position and momentum may be replaced by an exact equality, for suitably chosen measures of position and momentum uncertainty. This "exact" uncertainty relation is valid for_all_ pure states,…
We study the motion of a particle in a particular magnetic field configuration both classically and quantum mechanically. For flux-free radially symmetric magnetic fields defined on circular regions, we establish that particle escape speeds…
Within Bohm`s interpretation of quantum mechanics particles follow classical trajectories that are determined by the full solution of the time dependent Schroedinger equation. If this interpretation is consistent it must be possible to…
After summarizing three versions of trajectory-based quantum mechanics, it is argued that only the original formulation due to Bohm, which uses the Schr\"odinger wave function to guide the particles, can be readily extended to particles…
We propose that the Schrodinger equation results from applying the classical wave equation to describe the physical system in which subatomic particles play random motion, thereby leading to quantum mechanics. The physical reality described…
"Particle"-trajectories are defined as integrable $dx_\mu dp^\mu = 0$ paths in projective space. Quantum states evolving on such trajectories, open or closed, do not delocalise in $(x, p)$ projection, the phase associated with the…
We derive new solutions of the Schr\"odinger equation which describe the motion of particles in the Penning trap. These solutions are direct counterparts of classical orbits. They are obtained by injection of classical trajectories into the…
This paper presents a new approach to phase space trajectories in quantum mechanics. A Moyal description of quantum theory is used, where observables and states are treated as classical functions on a classical phase space. A quantum…
In classical theory, the trajectory of a particle is entirely predetermined by the complete set of initial conditions via dynamical laws. Based on this, we formulate a no-go theorem for the dynamics of classical particles, i.e., a Bell's…
A quantum mechanics representation based on position ($\vec{r}$), linear momentum($\vec{p}$) and energy($E$) eigenvalues is presented here. A set of equations, explicitly independent on wave function, was derived relating these observables.…
In the Entropic Dynamics (ED) approach to quantum theory the particles have well-defined positions but since they follow non differentiable Brownian trajectories they cannot be assigned an instantaneous momentum. Nevertheless, four…
The existence of precise particle trajectories in any quantum state is accounted for in a consistent way by allowing delocalization of the particle charge. The relativistic mass of the particle remains within a small volume surrounding a…
A semiclassical approximation is derived by using a family of wavepackets to map arbitrary wavefunctions into phase space. If the Hamiltonian can be approximated as linear over each individual wavepacket, as often done when presenting…