Related papers: Wave function as geometric entity

This paper presents new analytic solutions to the Dirac equation employing a recently introduced method that is based on the formulation of spinorial fields and their driving electromagnetic fields in terms of geometric algebras. A first…

The problem of classical particle in linear potential is studied by using the formalism of Hilbert space and tomographic probability distribution. The Liouville equation for this problem is solved by finding the density matrix satisfying…

Since the discovery of quantum mechanics, the fact that the wavefunction is defined on the $3\mathbf{n}$-dimensional configuration space rather than on the $3$-dimensional space has seemed uncanny to many, including Schr\"odinger, Lorentz,…

The Euler's equations describe the motion of inviscid fluid. In the case of shallow water, when a perturbative asymtotic expansion of the Euler's equations is taken (to a certain order of smallness of the scale parameters), relations to…

In a previous work we have described the classical structure and analyzed the interaction of the classical Dirac particle with uniform and oscillating electric and magnetic fields. In the present paper we consider the interaction of the…

We investigate the geometrical features of one-dimensional wave propagation, whose dynamics is described by the (2+1)-dimensional Lorentz group. We find many interesting geometrical ingredients such as spinorlike behavior of wave…

Roughly speaking a solitary wave is a solution of a field equation whose energy travels as a localised packet and which preserves this localisation in time. A soliton is a solitary wave which exhibits some strong form of stability so that…

With modern computers we can compute nuclear many-body wave functions with an astounding number of component, $ > 10^{10}$. But, aside from reproducing and/or predicting experiments, what do we learn from vectors with tens of billions of…

The fundamental solution of the Dirac equation for an electron in an electromagnetic field with harmonic dependence on space-time coordinates is obtained. The field is composed of three standing plane harmonic waves with mutually orthogonal…

Nonrelativistic quantum mechanics is commonly formulated in terms of wavefunctions (probability amplitudes) obeying the static and the time-dependent Schroedinger equations (SE). Despite the success of this representation of the quantum…

We reduce Dirac's spinor formalism for a spin 1/2 particle to a complex wavefunction description in curved spacetimes. We consider a localized fermionic particle in curved spacetimes and perform an expansion in terms of the acceleration and…

When a two-dimensional curved surface is conceived as a limiting case of a curved shell of equal thickness d, where the limit d\rightarrow0 is then taken, the well-known geometric potential is induced by the kinetic energy operator, in fact…

I address the question whether the wave function in quantum theory exists as a real (ontic) quantity or not. For this purpose, I discuss the essentials of the quantum formalism and emphasize the central role of the superposition principle.…

In this paper we calculate and visualize the dynamics of an ensemble of electrons trapping in an electrostatic wave of slowly increasing amplitude, illustrating that, despite disordering of particles in angle during the trapping transition…

A numerical approach to the problem of wave scattering by many small particles is developed under the assumptions k<<1, d>>a, where a is the size of the particles and d is the distance between the neighboring particles. On the wavelength…

Physical meaning and a duality of concepts of wave function, action functional, entropy, the Pointing vector, the Einstein tensor and so on can be disclosed by investigating the state of material systems such as thermodynamic and gas…

This article is based on the covariant causal set ($c$-causet) approach to discrete quantum gravity. A $c$-causet $x$ is a finite partially ordered set that has a unique labeling of its vertices. A rate of change on $x$ is described by a…

As a substitute for the current hypothesis of space-time continuity, we show the nature and the characteristics of a Schild's discrete space-time. With the wave perturbations of its metrical structure we formulate the working hypothesis…

Motivated by previous investigations on the radiative effects of the electric dipoles embedded in structured cavities, localization of electromagnetic waves in two dimensions is studied {\it ab initio} for a system consisting of many…

The use of operator methods of algebraic nature is shown to be a very powerful tool to deal with different forms of relativistic wave equations. The methods provide either exact or approximate solutions for various forms of differential…