Related papers: Solvable relativistic quantum dots with vibrationa…
A new relativistic description of quantum electrodynamics is presented. Guideline of the theory is the Klein-Gordon equation, which is reformulated to consider spin effects. This is achieved by a representation of relativistic vectors with…
A supersymmetric technique for the bound-state solutions of the s-wave Klein--Gordon equation with equal scalar and vector standard Eckart type potential is proposed. Its exact solutions are obtained. Possible generalization of our approach…
One examines the infinitely deep quantum cavity, also known as the quantum infinite square well, within the framework of the real Hilbert space. The solutions are considered in terms of complex wave functions, and also in terms of…
The covariant Klein-Gordon equation requires twice the boundary conditions of the Schrodinger equation and does not have an accepted single-particle interpretation. Instead of interpreting its solution as a probability wave determined by an…
A simple 1-D relativistic model for a diatomic molecule with a double point interaction potential is solved exactly in a constant electric field. The Weyl-Titchmarsh-Kodaira method is used to evaluate the spectral density function, allowing…
In the present study, Kummer's eigenvalue spectra from a charged spinless particle located at spherical pseudo-dot of the form $r^2+1/r^2$ is reported. Here, it is shown how confluent hypergeometric functions have principal quantum numbers…
In this work we discuss the deformed relativistic wave equations, namely the Klein--Gordon and Dirac equations in a Doubly Special Relativity scenario. We employ what we call a geometric approach, based on the geometry of a curved momentum…
In this article, we investigate the bound state solution of the Klein Gordon equation under mixed vector and scalar coupling of an energy-dependent deformed Hulth\'en potential in D-dimensions. We obtain a transcendental equation after we…
We consider the Klein--Gordon equation associated with the Laplace--Beltrami operator $\Delta$ on real hyperbolic spaces of dimension $n\!\ge\!2$; as $\Delta$ has a spectral gap, the wave equation is a particular case of our study. After a…
We seek to introduce a mathematical method to derive the Klein-Gordon equation and a set of relevant laws strictly, which combines the relativistic wave functions in two inertial frames of reference. If we define the stationary state wave…
This article develops a variational formulation for the relativistic Klein-Gordon equation. The main results are obtained through an extension of the classical mechanics approach to a more general context, which in some sense, includes the…
Whether monochromatic, pulsed, or even constant and crossed, the field used to describe the interaction of charged fermions with an intense laser beam is mainly assumed to be of plane-wave form. We consider a simple extension to plane-wave…
We examine the nonperturbative effect of maximum momentum on the relativistic wave equations. In momentum representation, we obtain the exact eigen-energies and wavefunctions of one-dimensional Klein-Gordon and Dirac equation with linear…
Positive-energy solutions of the Klein-Gordon equation form a Hilbert space of holomorphic functions on the future tube. This domain is interpreted as an extended phase space for the associated classical particle, the extra dimensions being…
Covariant classical particle dynamics is described, and the associated covariant relativistic particle quantum mechanics is derived. The invariant symmetric bracket is defined on the space of quantum amplitudes, and its relation to a…
We describe a procedure naturally associating relativistic Klein-Gordon equations in static curved spacetimes to non-relativistic quantum motion on curved spaces in the presence of a potential. Our procedure is particularly attractive in…
Using a variation of the celebrated Volkov solution, the Klein-Gordon equation for a charged particle is reduced to a set of ordinary differential equations, exactly solvable in specific cases. The new quantum relativistic structures can…
The ground state and the excitation spectrum of strongly correlated electrons in quantum dots are investigated. An analytical solution is constructed by exact diagonalization of the Hamiltonian in terms of the $N$-particle eigenmodes.
We reconsider the Rovelli-Smolin model of gravity coupled to the Klein-Gordon time field with an eye towards capturing the degrees of freedom of the scalar field lost in the framework in which time is deparametrized by the scalar field.…
Bound states generated by K coupled PT-symmetric square wells are studied in a series of models where the Hamiltonians are assumed $R-$pseudo-Hermitian and $R^2-$symmetric. Specific rotation-like generalized parities $R$ are considered such…