Klein-Gordon Particle Research Articles

Klein–Gordon particles in symmetrical well potential

An approximate analytical solution of the Klein–Gordon equation for the equal scalar and vector symmetrical well potential is presented in this study. The energy eigenvalue equation and corresponding wave functions for arbitrary n and l quantum states are obtained using the Nikiforov–Uvarov method in the closed form. Some special cases are also investigated.

On the correspondence between quantum and classical variational principles

Classical variational principles can be deduced from quantum variational principles via formal reparameterization of the latter. It is shown that such reparameterization is possible without invoking any assumptions other than classicality and without appealing to dynamical equations. As examples, first principle variational formulations of classical point-particle and cold-fluid motion are derived from their quantum counterparts for Schrödinger, Pauli, and Klein–Gordon particles.

Spinless relativistic particle in energy-dependent potential and normalization of the wave function

Abstract The problem of normalization related to a Klein-Gordon particle subjected to vector plus scalar energy-dependent potentials is clarified in the context of the path integral approach. In addition the correction relating to the normalizing constant of wave functions is exactly determined. As examples, the energy dependent linear and Coulomb potentials are considered. The wave functions obtained via spectral decomposition, were found exactly normalized.

Complex statistics and diffusion in nonlinear disordered particle chains.

We investigate dynamically and statistically diffusive motion in a Klein-Gordon particle chain in the presence of disorder. In particular, we examine a low energy (subdiffusive) and a higher energy (self-trapping) case and verify that subdiffusive spreading is always observed. We then carry out a statistical analysis of the motion, in both cases, in the sense of the Central Limit Theorem and present evidence of different chaos behaviors, for various groups of particles. Integrating the equations of motion for times as long as 10(9), our probability distribution functions always tend to Gaussians and show that the dynamics does not relax onto a quasi-periodic Kolmogorov-Arnold-Moser torus and that diffusion continues to spread chaotically for arbitrarily long times.

Klein-Gordon particle in a one-dimensional box with a moving wall

Relativistic treatment of a quantum mechanical massive particle in a one-dimensional box with one moving wall is presented using the Klein–Gordon equation. Despite the time dependence of the boundary, a separation of variables has been achieved for uniform wall motion by first transforming to a fixed boundary and subsequently introducing a new time coordinate. Exact solutions for both single variable differential equations have been obtained.

Scattering of Klein–Gordon particles by a Kink-like potential

The Klein–Gordon equation for the non-minimal vector and a scalar Kink-like potential is solved in terms of the hypergeometric functions. The scattering problem, i.e. the transmission and reflection coefficients, is studied as well.

Mott scattering of a Klein-Gordon particle in an intense laser field

AbstractWe study the Mott scattering of charged spinless particles in the presence of an intense plane wave laser pulse with fixed propagation direction and arbitrary duration and shape. We derive two equivalent forms of the transition amplitude and we discuss the relation between the respective results obtained in the case of a laser pulse and the monochromatic case. We obtain the condition defining the boundaries of the “bright” domain (the domain of allowed values in the energy-direction space of the scattered particle) and we illustrate our results with numerical examples.

Relativistic spinless particles in the generalized asymmetric Woods–Saxon potential

In this study, the Klein–Gordon equation in one spatial dimension is solved exactly for the generalized asymmetric Woods–Saxon potential containing the various forms of physical potentials, such as the usual Woods–Saxon, asymmetric Hulthen, usual Hulthen, asymmetric cusp and usual cusp potentials. The solutions that describe the scattering and bound states of the Klein–Gordon particles are obtained in terms of the hypergeometric functions. Using the boundary conditions satisfied by the wave functions and considering the asymptotic behavior of the wave functions, we examine a condition for the transmission resonances of the relativistic spinless particles in view of the generalized asymmetric Woods–Saxon potential. Furthermore, dependence of the transmission coefficients on the generalized asymmetric Woods–Saxon potential parameters as well as the energies of Klein–Gordon particles is investigated numerically by using the Mathematica Software.

Effects of external fields on a two-dimensional Klein—Gordon particle under pseudo-harmonic oscillator interaction

We study the effects of the perpendicular magnetic and Aharonov—Bohm (AB) flux fields on the energy levels of a two-dimensional (2D) Klein—Gordon (KG) particle subjected to an equal scalar and vector pseudo-harmonic oscillator (PHO). We calculate the exact energy eigenvalues and normalized wave functions in terms of chemical potential parameter, magnetic field strength, AB flux field, and magnetic quantum number by means of the Nikiforov—Uvarov (NU) method. The non-relativistic limit, PHO, and harmonic oscillator solutions in the existence and absence of external fields are also obtained.

Zitterbewegungof Klein-Gordon particles and its simulation by classical systems

The Klein-Gordon equation is used to calculate the Zitterbewegung (ZB, trembling motion) of spin-zero particles in absence of fields and in the presence of an external magnetic field. Both Hamiltonian and wave formalisms are employed to describe ZB and their results are compared. It is demonstrated that, if one uses wave packets to represent particles, the ZB motion has a decaying behavior. It is also shown that the trembling motion is caused by an interference of two sub-packets composed of positive and negative energy states which propagate with different velocities. In the presence of a magnetic field the quantization of energy spectrum results in many interband frequencies contributing to ZB oscillations and the motion follows a collapse-revival pattern. In the limit of non-relativistic velocities the interband ZB components vanish and the motion is reduced to cyclotron oscillations. The exact dynamics of a charged Klein-Gordon particle in the presence of a magnetic field is described on an operator level. The trembling motion of a KG particle in absence of fields is simulated using a classical model proposed by Morse and Feshbach -- it is shown that a variance of a Gaussian wave packet exhibits ZB oscillations.

A Klein–Gordon particle captured by embedded curves

In the present work, a Klein–Gordon particle with singular interactions supported on embedded curves on Riemannian manifolds is discussed from a more direct and physical perspective, via the heat kernel approach. It is shown that the renormalized problem is well-defined, and the ground state energy is unique and finite. The renormalization group invariance of the model is discussed, and it is observed that the model is asymptotically free.

Transport Properties of the Universal Quantum Equation

The universal quantum equation (UQE) is found to describe the transport properties of the quantum particles. This equation describes a wave equation interacting with constant scalar and vector potentials propagating in spacetime. A new transformation that sends the Schrödinger equation with a potential energy to Dirac's equation is proposed. The Cattaneo telegraph equation as well as a one-dimensional UQE are compatible with our recently proposed generalized continuity equations. Furthermore, a new wave equation resulted from the invariance of the UQE under the post-Galilean transformations is derived. This equation is found to govern a Klein—Gordon's particle interacting with a photon-like vector field (ether) whose magnitude is proportional to the particle's mass.

Stochastic quantization method for spinless relativistic particles in two wave fields

Using the Parisi and Wu stochastic quantization method, the Green's function for a Klein–Gordon particle subjected to the action of two plane electromagnetic waves propagating along particular directions is determined exactly thanks to a perturbative treatment. The calculation is performed in the phase space.

Superstatistics approach to path integral for a relativistic particle

Superstatistics permits the calculation of the Feynman propagator of a relativistic particle in a novel way from a superstatistical average over non-relativistic single-particle paths. We illustrate this for the Klein-Gordon particle in the Feshbach-Villars representation, and for the Dirac particle in the Schroedinger-Dirac representation. As a byproduct we recover the worldline representation of Klein-Gordon and Dirac propagators, and discuss the role of the smearing distributions in fixing the reparametrization freedom. The emergent relativity picture that follows from our approach together with a novel representation of the Lorentz group for the Feshbach-Villars particle are also discussed.

Renormalized interaction of relativistic bosons with delta function potentials

We study the interaction of mutually noninteracting Klein–Gordon particles with localized sources on stochastically complete Riemannian surfaces. This asymptotically free theory requires regularization and coupling constant renormalization. Renormalization is performed nonperturbatively using the orthofermion algebra technique and the principal operator Φ is found. The principal operator is then used to obtain the bound state spectrum, in terms of binding energies to single Dirac-delta function centers. The heat kernel method allows us to generalize this procedure to compact and Cartan–Hadamard type Riemannian manifolds. We make use of upper and lower bounds on the heat kernel to constrain the ground state energy from below, thus confirming that our neglect of pair creation is justified for certain ranges of parameters in the problem.

Path Integral Treatment of a Dirac Particle in a Weak Gravitational Plane Wave

The Green functions for Klein-Gordon and Dirac particles in a weak gravitational field are determined exactly by the path integral formalism. By using simple changes, it is shown that the classical trajectories play an important role in determining these Green functions

Path integral solutions for Klein–Gordon particle in vector plus scalar generalized Hulthén and Woods–Saxon potentials

The Green’s function for a Klein–Gordon particle under the action of vector plus scalar deformed Hulthén and Woods–Saxon potentials is evaluated by exact path integration. Explicit path integration leads to the Green’s function for different shapes of the potentials. From the singularities of the latter Green’s function, the bound states are extracted. For q≥1 and (1/α)ln q<r<∞, the analytic expression of the energy spectrum and the normalized wave functions for the l states are obtained within the framework of an approximation to the centrifugal term. When the deformation parameter q is 0<q<1 or q<0, it is found that the quantization conditions are transcendental equations involving the hypergeometric function that require a numerical solution for the s-state energy levels. Particular cases of these potentials are also discussed briefly.

Relativistic Klein–Gordon charge effects by information-theoretic measures

The charge spreading of the ground and excited states of Klein–Gordon particles moving in a Coulomb potential is quantitatively analysed by means of ordinary moments and the Heisenberg measure as well as by using the most relevant information-theoretic measures of global (Shannon entropic power) and local (Fisher information) types. The dependence of these complementary quantities on the nuclear charge Z and the quantum numbers characterizing the physical states is carefully discussed. The comparison of relativistic Klein–Gordon and non-relativistic Schrödinger values is made. Non-relativistic limits at large principal quantum number n and for small values of Z are also reached.

Scattering of a Klein–Gordon particle by a Hulthén potential

The Klein–Gordon equation in the presence of a spatially one-dimensional Hulthén potential is solved exactly and the scattering solutions are obtained in terms of hypergeometric functions. The transmission coefficient is derived by the matching conditions on the wave functions and the conditions for the existence of transmission resonances are investigated. It is shown how the zero-reflection condition depends on the shape of the potential.

Transmission resonance for a Klein-Gordon particle in one-dimensional Hulthén potential barrier

The Klein-Gordon equation in the presence of a spatially one-dimensional Hulthén potential barrier is solved and the scattering state solutions are obtained in terms of the hypergeometric functions. Both the reflection coefficient and transmission coefficient are calculated from the boundary condition of Klein-Gordon equation and the conditions for transmission resonance are then derived.The result shows that when the reflection coefficient is zero the transmission resonance takes place.