Klein-Gordon Equation and Wave Function for Free Particle in Rindler Space-Time

Klein-Gordon equation is a relativistic wave equation. It treats spinless particle. The wave functioncannot use as a probability amplitude. We made Klein-Gordon equation in Rindler space-time. In this paper,we make free particle’s wave function as the solution of Klein-Gordon equation in Rindler space-time.

The radiation of a spin-free particle in the field of a plane electromagnetic wave

In this paper, we obtained a solution for the equation of motion of a charged spinless particle in the field of a plane electromagnetic wave. Relativistic expressions for the cross section of Compton scattering by a charged particle of spin 0 interacting with the field of a plane electromagnetic wave are calculated. Numerical simulation of the total probability of radiation as the function of the electromagnetic wave amplitude is carried out. The radiation probability is found to be consistent with the total cross section for Compton scattering by a charged particle of spin 0.

Entropic system in the relativistic Klein-Gordon Particle

The solutions of Kratzer potential plus Hellmann potential was obtained under the Klein-Gordon equation via the parametric Nikiforov-Uvarov method. The relativistic energy and its corresponding normalized wave functions were fully calculated. The theoretic quantities in terms of the entropic system under the relativistic Klein-Gordon equation (a spinless particle) for a Kratzer-Hellmann’s potential model were studied. The effects of a and b respectively (the parameters in the potential that determine the strength of the potential) on each of the entropy were fully examined. The maximum point of stability of a system under the three entropies was determined at the point of intersection between two formulated expressions plotted against a as one of the parameters in the potential. Finally, the popular Shannon entropy uncertainty relation known as Bialynick-Birula, Mycielski inequality was deduced by generating numerical results.

ONE-PARTICLE WAVE FUNCTIONS IN THE RELATIONAL PARADIGM

We discuss a quantum description of free particles in pseudo-Finslerian momentum spaces appearing in one of relational approaches to physics and geometry of space-time. It is shown that, for wave functions of such particles, we can define an invariant unitary scalar product which ensures the standard quantum mechanical probabilistic interpretation. As the simplest example, the description of a spinless particle is considered.

Spinless Particle with Darwin–Cox Structure in an External Coulomb Field

Generalized Klein–Fock–Gordon equation for a spinless particle with the Darwin–Cox structure, which takes into account distribution of the electric charge of a particle inside a finite spherical region is studied in presence of an external Coulomb field. There have been constructed exact Frobenius type solutions of the derived equations, convergence of the relevant power series with 8-term recurrent relations has been studied. As an analytical quantization rule is taken the so-called transcendency conditions. It provides us with a 4-th order algebraic equation with respect to energy values, which has four sets of roots. One set of roots, 0 < En;k < 1, depending on the angular momentum n = 0; 1; 2; : : : and the main quantum number n = 0; 1; 2; : : : may be interpreted as corresponding to some bound states of the particle in a Coulomb field. In the same manner, a generalized nonrelativistic Schr¨odinger equation for such a particle is studied, the final results are similar.

Gravitational Interaction of Cosmic String with Spinless Particle

We consider the gravitational interaction of spinless relativistic particle and infinitely thin cosmic string within the classical linearized-theory framework. We compute the particle’s motion in the transverse (to the unperturbed string) plane. The reciprocal action of the particle on the cosmic string is also investigated. We derive the retarded solution which includes the longitudinal (with respect to the unperturbed-particle motion) and totally-transverse string perturbations.

Klein‐Gordon and Schrödinger equations for a free particle in the rest frame

A system of two equations is found that has solutions which coincide with the solutions of the Klein‐Gordon equation in the rest frame. This system includes the Schrödinger equation for a free neutral spinless particle. Using the Schrödinger equation as an additional condition for solving the Klein‐Gordon equation in the rest frame leads to two Helmholtz equations. Helmholtz equations can be solved by specifying a particle model and boundary conditions. One of the Helmholtz equations leads to discreteness of the rest masses of relativistic particles.

Quantum Cosmologies Under Geometrical Unification of Gravity and Dark Energy

A Friedmann–Robertson–Walker Universe was studied with a dark energy component represented by a quintessence field. The Lagrangian for this system, hereafter called the Friedmann–Robertson–Walker–quintessence (FRWq) system, was presented. It was shown that the classical Lagrangian reproduces the usual two (second order) dynamical equations for the radius of the Universe and for the quintessence scalar field, as well as a (first order) constraint equation. Our approach naturally unified gravity and dark energy, as it was obtained that the Lagrangian and the equations of motion are those of a relativistic particle moving on a two-dimensional, conformally flat spacetime. The conformal metric factor was related to the dark energy scalar field potential. We proceeded to quantize the system in three different schemes. First, we assumed the Universe was a spinless particle (as it is common in literature), obtaining a quantum theory for a Universe described by the Klein–Gordon equation. Second, we pushed the quantization scheme further, assuming the Universe as a Dirac particle, and therefore constructing its corresponding Dirac and Majorana theories. With the different theories, we calculated the expected values for the scale factor of the Universe. They depend on the type of quantization scheme used. The differences between the Dirac and Majorana schemes are highlighted here. The implications of the different quantization procedures are discussed. Finally, the possible consequences for a multiverse theory of the Dirac and Majorana quantized Universe are briefly considered.

Effects of a non-Hermitian potential on the Landau quantization

In this work, we solve the time-independent Schrödinger equation for a Landau system modulated by a non-Hermitian Hamiltonian. The system consists of a spinless particle in a uniform magnetic field submitted to action of a non-[Formula: see text] symmetric complex potential. Although the Hamiltonian is neither Hermitian nor [Formula: see text]-symmetric, we find that the Landau problem under study exhibits an entirely real energy spectrum.