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The one-dimensional Klein-Gordon equation is solved for the PT-symmetric generalized Hulthen potential in the scalar coupling scheme. The relativistic bound-state energy spectrum and the corresponding wave functions are obtained by using…
The relativistic problem of spinless particle subject to a Kratzer potential is analyzed. Bound state solutions for the s-wave are found by separating the Klein-Gordon equation in two parts, unlike the similar works in the literature, which…
The relativistic wave equations determine the dynamics of quantum fields in the context of quantum field theory. One of the conventional tools for dealing with the relativistic bound-state problem is the Klein-Fock-Gordon equation. In this…
The s-wave Klein-Gordon equation for the bound states is separated in two parts to see clearly the relativistic contributions to the solution in the non-relativistic limit. The reliability of the model is discussed with the specifically…
Analytical solutions of the Klein-Gordon equation are obtained by reducing the radial part of the wave equation to a standard form of a second order differential equation. Differential equations of this standard form are solvable in terms…
The approximate analytic bound state solutions of the Klein-Gordon equation with equal scalar and vector exponential-type potentials including the centrifugal potential term are obtained for any arbitrary orbital angular momentum number l…
A detailed consideration of the Klein-Gordon equation in relativistic quantum mechanics is presented in order to offer more clarity than many standard approaches. The equation is frequently employed in the research literature, even though…
We consider for the first time the solutions of Klein-Gordon equation in gravitational field of {\em a massive} point source in GR. We examine numerically the basic bounded quantum state and the next few states in the discrete spectrum for…
We solve the relativistic Klein--Gordon equation for a light particle gravitationally bound to a heavy central mass, with the gravitational interaction prescribed by the metric of a spherically symmetric space-time. Metrics are considered…
Extended quantum mechanics using non-Hermitian, pseudo-Hermitian Hamiltonians is briefly reviewed. Supersymmetric regularizations, solvable simulations and large-N expansion techniques are recollected as suitable means for the study of…
This dissertation discusses solutions to the nonlinear Klein-Gordon equation with symmetric and asymmetric double-well potentials, focusing on the collapse and collision of bubbles and critical phenomena found therein. A new method is…
The relativistic quantum dynamics of an electrically charged particle subject to the Klein-Gordon oscillator and the Coulomb potential is investigated. By searching for relativistic bound states, a particular quantum effect can be observed:…
Within this article one finds the statement of the Klein-Gordon problem within the real Hilbert space formalism ($\mathbbm R$HS) in terms of complex wave functions, and in terms of quaternionic wave functions as well. The complex…
The D-dimensional Klein-Gordon (KG) wave equation with unequal scalar and time-like vector Cornell interactions is solved by the Laplace transform method. In fact, we obtained the bound state energy eigenvalues of the spinless relativistic…
In quantum theory, bound states are described by eigenvalue equations, which usually cannot be solved exactly. However, some simple general theorems allow to derive rigorous statements about the corresponding solutions, that is, energy…
The Klein-Gordon system describing three scalar particles without interaction is cast into a new form, by transformation of the momenta. Two redundant degrees of freedom are eliminated; we are left with a covariant equation for a reduced…
In this study, we solve the Klein-Gordon equation with equal scalar and vector q-deformed hyperbolic modified P\"{o}schl-Teller potential. The explicit expressions of bound state spectra and the normalized eigenfunctions for s-wave bound…
A solvable 2-dimensional conformally invariant midi-superspace model for black holes is obtained by imposing spherical symmetry in 4-dimensional conformally invariant Einstein gravity. The Wheeler-DeWitt equation for the theory is solved…
We present an approximate analytic solution of the Klein-Gordon equation in the presence of equal scalar and vector generalized deformed hyperbolic potential functions by means of parameteric generalization of the Nikiforov-Uvarov method.…
We solve the Klein-Gordon equation in any $D$-dimension for the scalar and vector general Hulth\'{e}n-type potentials with any $l$ by using an approximation scheme for the centrifugal potential. Nikiforov-Uvarov method is used in the…