Related papers: Solvable Two-Body Dirac Equation as a Potential Mo…
The two-body problem with a central interaction on simply connected constant curvature spaces of an arbitrary dimension is considered. The explicit expression for the quantum two-body Hamiltonian via a radial differential operator and…
We use Dirac's constraint dynamics to obtain a Hamiltonian formulation of the relativistic N-body problem in a separable two-body basis in which the particles interact pair-wise through scalar and vector interactions. The resultant N-body…
Physical properties of the Cornell potential in the complex-mass scheme are investigated. Two exact asymptotic solutions of relativistic wave equation for the coulombic and linear components of the potential are used to derive the resonance…
We consider the Dirac equations in polar form proving that they can equivalently be re-configured into a system of equations consisting of derivatives of the velocity density plus the Hamilton-Jacobi equation, giving the momentum in terms…
We obtain for the attractive Dirac delta-function potential in two-dimensional quantum mechanics a renormalized formulation that avoids reference to a cutoff and running coupling constant. Dimensional transmutation is carried out before…
We obtain exact solutions of Dirac equation at zero kinetic energy for radial power-law relativistic potentials. It turns out that these are the relativistic extension of a subclass of exact solutions of Schrodinger equation with two-term…
Starting from a model of an elastic medium, we derive equations of motion that are identical in form to Dirac's equation for a spin 1/2 particle with mass, coupled to electromagnetic and gravitational interactions. The mass and…
The two-body Coulomb scattering problem is solved using the standard complex scaling method. The explicit enforcement of the scattering boundary condition is avoided. Splitting of the scattering wave function based on the Coulomb modified…
A relativistic two-body wave equation, local in configuration space, is derived from the Bethe-Salpeter equation for two scalar particles bound by a scalar Coulomb interaction. The two-body bound-state wave equation is solved analytically,…
A recently proposed algorithm to obtain global solutions of the double confluent Heun equation is applied to solve the quantum mechanical problem of finding the energies and wave functions of a particle bound in a potential sum of a…
In the present work we establish a simple relation between the Dirac equation with a scalar and an electromagnetic potentials in a two-dimensional case and a pair of decoupled Vekua equations. In general these Vekua equations are bicomplex.…
The Dirac equation has resided among the greatest successes of modern physics since its emergence as the first quantum mechanical theory fully compatible with special relativity. This compatibility ensures that the expectation value of the…
A Lorentz-covariant system of wave equations is formulated for a quantum-mechanical three-body system in one space dimension, comprised of one photon and two identical massive spin one-half Dirac particles, which can be thought of as two…
The Dirac oscillator coupled to an external two-component field can retain its solvability, if couplings are appropriately chosen. This provides a new class of integrable systems. A simplified way of solution is given, by recasting the…
Given a spatially dependent mass distribution we obtain potential functions for exactly solvable nonrelativistic problems. The energy spectrum of the bound states and their wavefunctions are written down explicitly. This is accomplished by…
We develop a systematic procedure for constructing quantum many-body problems whose spectrum can be partially or totally computed by purely algebraic means. The exactly-solvable models include rational and hyperbolic potentials related to…
We find the exact bound-state solutions and normalization constant for the Dirac equation with scalar-vector-pseudoscalar interaction terms for the generalized Hulth\'{e}n potential in the case where we have a particular mass function…
An exact solution is given for a two-dimensional model of a Coulomb gas, more general than the previously solved ones. The system is made of a uniformly charged background, positive particles, and negative particles, on the surface of a…
We study the problem of two Dirac particles interacting through non-relativistic potentials and confined to a two-dimensional sheet, which is the relevant case for graphene layers. The two-body problem cannot be mapped into that of a single…
In case of spinless particles there appear additional (singular) solutions in the framework of relativistic Klein-Gordon equation for Coulomb potential. These solutions obey to all requirements of quantum mechanical general principles.…