Related papers: On the Existence of Additional (Hydrino) states in…
We discuss the tightly bound (hydrino) solution of the Klein-Gordon equation for the Coulomb potential in 3 dimensions. We show that a similarly tightly bound state occurs for the Dirac equation in 2 dimensions. These states are unphysical…
The Klein-Gordon equation of the hydrogen atom has a low-lying eigenstate, called hydrino state, with square integrable wavefunction. The corresponding spinor solution of Dirac's equation is not square integrable. For this reason the…
The Dirac equation with the Coulomb potential is studied. It is shown that there exists a new invariant in addition to the known Dirac and Johnson-Lippman ones. The solution of the Dirac equation, using the generalized invariant, and…
Some recent work has attempted to show that the singular solutions which are known to occur in the Dirac description of spin-1/2 Aharonov-Bohm scattering can be eliminated by the inclusion of strongly repulsive potentials inside the flux…
The spin-1/2 Aharonov-Bohm problem is examined in the Galilean limit for the case in which a Coulomb potential is included. It is found that the application of the self-adjoint extension method to this system yields singular solutions only…
Solutions of the Dirac equation for an electron in the Coulomb potential are obtained using operator invariants of the equation, namely the Dirac, Johnson-Lippmann and recently found new invariant. It is demonstrated that these operators…
Seeking for a relativistic generalisation of the non-relativistic Schroedinger equation, one very soon arrives at equations with a square-root operator by having applied the quantum mechanical correspondence principle to the formula of…
The Dirac equation for a massive spin-1/2 field in a central potential V in three dimensions is studied without fixing a priori the functional form of V. The second-order equations for the radial parts of the spinor wave function are shown…
One more mode developed to get eigen energies and states for the one-electron Dirac's equation with spherically symmetric bound potential. For the particular case of the Coulomb potential it was shown that the method is free of so called…
There exists a Klein-Gordon-like equation for a spin-1/2 particle in an electromagnetic field with 2-spinors as wave functions that is a direct consequence of the corresponding Dirac equation. Thus, it reproduces the same binding energies…
The quantum predictions for a single nonrelativistic spin-1/2 particle can be reproduced by noncontextual hidden variables. Here we show that quantum contextuality for a relativistic electron moving in a Coulomb potential naturally emerges…
The problem of a spin 1 charged particle with electromagnetic polarizability, obeying a generalized 15-component quantum mechanical equation, is investigated in presence of the external Coulomb potential. With the use of the Wigner's…
The problem of a spinless particle subject to a general mixing of vector and scalar inversely linear potentials in a two-dimensional world is analyzed. Exact bounded solutions are found in closed form by imposing boundary conditions on the…
This paper presents a relativistic symmetrical interpretation of the Dirac equation in 1+1 dimensions which predicts no zitterbewegung for a free spin-1/2 particle. This could resolve the longstanding puzzle of zitterbewegung in…
In this study, the Majorana equation for particles with arbitrary spin is solved for a half-integer spin free particle. The solution for the fundamental state, corresponding to the reference frame in which the particle is at rest, is…
Solutions to the Dirac equation are constructed for a massless charged fermion in Coulomb and Aharonov--Bohm potentials in 2+1 dimensions. The Dirac Hamiltonian on this background is singular and needs a one-parameter self-adjoint…
We present exact analytical solutions of the Dirac equation in $(1+1)$-dimensions for the generalized Kratzer potential by taking the pseudoscalar interaction term as an attractive Coulomb potential. We study the problem for a particular…
Klein-Gordon and Dirac equations are the motion equations for relativistic particles with spin 0 (so-called scalar particles) and 1/2 (electron/positron) respectively. For a free particle, the Dirac equation is derived from the Klein-Gordon…
The general solution of the Dirac equation for quasi-two-dimensional electrons confined in an asymmetric quantum well, is found. The energy spectrum of such a system is exactly calculated using special unitary transformation and shown to…
The Klein-Gordon equation describes the wave-like behavior of spinless particles since it is Lorentz invariant. While it seemed initially ripe for explaining the electronic structure of the hydrogen atom, the lack of a unconditional…